---
_id: '15013'
abstract:
- lang: eng
text: We consider random n×n matrices X with independent and centered entries and
a general variance profile. We show that the spectral radius of X converges with
very high probability to the square root of the spectral radius of the variance
matrix of X when n tends to infinity. We also establish the optimal rate of convergence,
that is a new result even for general i.i.d. matrices beyond the explicitly solvable
Gaussian cases. The main ingredient is the proof of the local inhomogeneous circular
law [arXiv:1612.07776] at the spectral edge.
acknowledgement: Partially supported by ERC Starting Grant RandMat No. 715539 and
the SwissMap grant of Swiss National Science Foundation. Partially supported by
ERC Advanced Grant RanMat No. 338804. Partially supported by the Hausdorff Center
for Mathematics in Bonn.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Johannes
full_name: Alt, Johannes
id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87
last_name: Alt
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
citation:
ama: Alt J, Erdös L, Krüger TH. Spectral radius of random matrices with independent
entries. Probability and Mathematical Physics. 2021;2(2):221-280. doi:10.2140/pmp.2021.2.221
apa: Alt, J., Erdös, L., & Krüger, T. H. (2021). Spectral radius of random matrices
with independent entries. Probability and Mathematical Physics. Mathematical
Sciences Publishers. https://doi.org/10.2140/pmp.2021.2.221
chicago: Alt, Johannes, László Erdös, and Torben H Krüger. “Spectral Radius of Random
Matrices with Independent Entries.” Probability and Mathematical Physics.
Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/pmp.2021.2.221.
ieee: J. Alt, L. Erdös, and T. H. Krüger, “Spectral radius of random matrices with
independent entries,” Probability and Mathematical Physics, vol. 2, no.
2. Mathematical Sciences Publishers, pp. 221–280, 2021.
ista: Alt J, Erdös L, Krüger TH. 2021. Spectral radius of random matrices with independent
entries. Probability and Mathematical Physics. 2(2), 221–280.
mla: Alt, Johannes, et al. “Spectral Radius of Random Matrices with Independent
Entries.” Probability and Mathematical Physics, vol. 2, no. 2, Mathematical
Sciences Publishers, 2021, pp. 221–80, doi:10.2140/pmp.2021.2.221.
short: J. Alt, L. Erdös, T.H. Krüger, Probability and Mathematical Physics 2 (2021)
221–280.
date_created: 2024-02-18T23:01:03Z
date_published: 2021-05-21T00:00:00Z
date_updated: 2024-02-19T08:30:00Z
day: '21'
department:
- _id: LaEr
doi: 10.2140/pmp.2021.2.221
ec_funded: 1
external_id:
arxiv:
- '1907.13631'
intvolume: ' 2'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1907.13631
month: '05'
oa: 1
oa_version: Preprint
page: 221-280
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Probability and Mathematical Physics
publication_identifier:
eissn:
- 2690-1005
issn:
- 2690-0998
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Spectral radius of random matrices with independent entries
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2
year: '2021'
...
---
_id: '9912'
abstract:
- lang: eng
text: "In the customary random matrix model for transport in quantum dots with M
internal degrees of freedom coupled to a chaotic environment via \U0001D441≪\U0001D440
channels, the density \U0001D70C of transmission eigenvalues is computed from
a specific invariant ensemble for which explicit formula for the joint probability
density of all eigenvalues is available. We revisit this problem in the large
N regime allowing for (i) arbitrary ratio \U0001D719:=\U0001D441/\U0001D440≤1;
and (ii) general distributions for the matrix elements of the Hamiltonian of the
quantum dot. In the limit \U0001D719→0, we recover the formula for the density
\U0001D70C that Beenakker (Rev Mod Phys 69:731–808, 1997) has derived for a special
matrix ensemble. We also prove that the inverse square root singularity of the
density at zero and full transmission in Beenakker’s formula persists for any
\U0001D719<1 but in the borderline case \U0001D719=1 an anomalous \U0001D706−2/3
singularity arises at zero. To access this level of generality, we develop the
theory of global and local laws on the spectral density of a large class of noncommutative
rational expressions in large random matrices with i.i.d. entries."
acknowledgement: The authors are very grateful to Yan Fyodorov for discussions on
the physical background and for providing references, and to the anonymous referee
for numerous valuable remarks.
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- first_name: Yuriy
full_name: Nemish, Yuriy
id: 4D902E6A-F248-11E8-B48F-1D18A9856A87
last_name: Nemish
orcid: 0000-0002-7327-856X
citation:
ama: Erdös L, Krüger TH, Nemish Y. Scattering in quantum dots via noncommutative
rational functions. Annales Henri Poincaré . 2021;22:4205–4269. doi:10.1007/s00023-021-01085-6
apa: Erdös, L., Krüger, T. H., & Nemish, Y. (2021). Scattering in quantum dots
via noncommutative rational functions. Annales Henri Poincaré . Springer
Nature. https://doi.org/10.1007/s00023-021-01085-6
chicago: Erdös, László, Torben H Krüger, and Yuriy Nemish. “Scattering in Quantum
Dots via Noncommutative Rational Functions.” Annales Henri Poincaré . Springer
Nature, 2021. https://doi.org/10.1007/s00023-021-01085-6.
ieee: L. Erdös, T. H. Krüger, and Y. Nemish, “Scattering in quantum dots via noncommutative
rational functions,” Annales Henri Poincaré , vol. 22. Springer Nature,
pp. 4205–4269, 2021.
ista: Erdös L, Krüger TH, Nemish Y. 2021. Scattering in quantum dots via noncommutative
rational functions. Annales Henri Poincaré . 22, 4205–4269.
mla: Erdös, László, et al. “Scattering in Quantum Dots via Noncommutative Rational
Functions.” Annales Henri Poincaré , vol. 22, Springer Nature, 2021, pp.
4205–4269, doi:10.1007/s00023-021-01085-6.
short: L. Erdös, T.H. Krüger, Y. Nemish, Annales Henri Poincaré 22 (2021) 4205–4269.
date_created: 2021-08-15T22:01:29Z
date_published: 2021-12-01T00:00:00Z
date_updated: 2023-08-11T10:31:48Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00023-021-01085-6
ec_funded: 1
external_id:
arxiv:
- '1911.05112'
isi:
- '000681531500001'
file:
- access_level: open_access
checksum: 8d6bac0e2b0a28539608b0538a8e3b38
content_type: application/pdf
creator: dernst
date_created: 2022-05-12T12:50:27Z
date_updated: 2022-05-12T12:50:27Z
file_id: '11365'
file_name: 2021_AnnHenriPoincare_Erdoes.pdf
file_size: 1162454
relation: main_file
success: 1
file_date_updated: 2022-05-12T12:50:27Z
has_accepted_license: '1'
intvolume: ' 22'
isi: 1
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 4205–4269
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: 'Annales Henri Poincaré '
publication_identifier:
eissn:
- 1424-0661
issn:
- 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Scattering in quantum dots via noncommutative rational functions
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 22
year: '2021'
...
---
_id: '7512'
abstract:
- lang: eng
text: We consider general self-adjoint polynomials in several independent random
matrices whose entries are centered and have the same variance. We show that under
certain conditions the local law holds up to the optimal scale, i.e., the eigenvalue
density on scales just above the eigenvalue spacing follows the global density
of states which is determined by free probability theory. We prove that these
conditions hold for general homogeneous polynomials of degree two and for symmetrized
products of independent matrices with i.i.d. entries, thus establishing the optimal
bulk local law for these classes of ensembles. In particular, we generalize a
similar result of Anderson for anticommutator. For more general polynomials our
conditions are effectively checkable numerically.
acknowledgement: "The authors are grateful to Oskari Ajanki for his invaluable help
at the initial stage of this project, to Serban Belinschi for useful discussions,
to Alexander Tikhomirov for calling our attention to the model example in Section
6.2 and to the anonymous referee for suggesting to simplify certain proofs. Erdös:
Partially funded by ERC Advanced Grant RANMAT No. 338804\r\n"
article_number: '108507'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- first_name: Yuriy
full_name: Nemish, Yuriy
id: 4D902E6A-F248-11E8-B48F-1D18A9856A87
last_name: Nemish
orcid: 0000-0002-7327-856X
citation:
ama: Erdös L, Krüger TH, Nemish Y. Local laws for polynomials of Wigner matrices.
Journal of Functional Analysis. 2020;278(12). doi:10.1016/j.jfa.2020.108507
apa: Erdös, L., Krüger, T. H., & Nemish, Y. (2020). Local laws for polynomials
of Wigner matrices. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2020.108507
chicago: Erdös, László, Torben H Krüger, and Yuriy Nemish. “Local Laws for Polynomials
of Wigner Matrices.” Journal of Functional Analysis. Elsevier, 2020. https://doi.org/10.1016/j.jfa.2020.108507.
ieee: L. Erdös, T. H. Krüger, and Y. Nemish, “Local laws for polynomials of Wigner
matrices,” Journal of Functional Analysis, vol. 278, no. 12. Elsevier,
2020.
ista: Erdös L, Krüger TH, Nemish Y. 2020. Local laws for polynomials of Wigner matrices.
Journal of Functional Analysis. 278(12), 108507.
mla: Erdös, László, et al. “Local Laws for Polynomials of Wigner Matrices.” Journal
of Functional Analysis, vol. 278, no. 12, 108507, Elsevier, 2020, doi:10.1016/j.jfa.2020.108507.
short: L. Erdös, T.H. Krüger, Y. Nemish, Journal of Functional Analysis 278 (2020).
date_created: 2020-02-23T23:00:36Z
date_published: 2020-07-01T00:00:00Z
date_updated: 2023-08-18T06:36:10Z
day: '01'
department:
- _id: LaEr
doi: 10.1016/j.jfa.2020.108507
ec_funded: 1
external_id:
arxiv:
- '1804.11340'
isi:
- '000522798900001'
intvolume: ' 278'
isi: 1
issue: '12'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1804.11340
month: '07'
oa: 1
oa_version: Preprint
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Journal of Functional Analysis
publication_identifier:
eissn:
- '10960783'
issn:
- '00221236'
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local laws for polynomials of Wigner matrices
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 278
year: '2020'
...
---
_id: '14694'
abstract:
- lang: eng
text: We study the unique solution m of the Dyson equation \( -m(z)^{-1} = z\1 -
a + S[m(z)] \) on a von Neumann algebra A with the constraint Imm≥0. Here, z lies
in the complex upper half-plane, a is a self-adjoint element of A and S is a positivity-preserving
linear operator on A. We show that m is the Stieltjes transform of a compactly
supported A-valued measure on R. Under suitable assumptions, we establish that
this measure has a uniformly 1/3-Hölder continuous density with respect to the
Lebesgue measure, which is supported on finitely many intervals, called bands.
In fact, the density is analytic inside the bands with a square-root growth at
the edges and internal cubic root cusps whenever the gap between two bands vanishes.
The shape of these singularities is universal and no other singularity may occur.
We give a precise asymptotic description of m near the singular points. These
asymptotics generalize the analysis at the regular edges given in the companion
paper on the Tracy-Widom universality for the edge eigenvalue statistics for correlated
random matrices [the first author et al., Ann. Probab. 48, No. 2, 963--1001 (2020;
Zbl 1434.60017)] and they play a key role in the proof of the Pearcey universality
at the cusp for Wigner-type matrices [G. Cipolloni et al., Pure Appl. Anal. 1,
No. 4, 615--707 (2019; Zbl 07142203); the second author et al., Commun. Math.
Phys. 378, No. 2, 1203--1278 (2020; Zbl 07236118)]. We also extend the finite
dimensional band mass formula from [the first author et al., loc. cit.] to the
von Neumann algebra setting by showing that the spectral mass of the bands is
topologically rigid under deformations and we conclude that these masses are quantized
in some important cases.
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Johannes
full_name: Alt, Johannes
id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87
last_name: Alt
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
citation:
ama: 'Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral
bands, edges and cusps. Documenta Mathematica. 2020;25:1421-1539. doi:10.4171/dm/780'
apa: 'Alt, J., Erdös, L., & Krüger, T. H. (2020). The Dyson equation with linear
self-energy: Spectral bands, edges and cusps. Documenta Mathematica. EMS
Press. https://doi.org/10.4171/dm/780'
chicago: 'Alt, Johannes, László Erdös, and Torben H Krüger. “The Dyson Equation
with Linear Self-Energy: Spectral Bands, Edges and Cusps.” Documenta Mathematica.
EMS Press, 2020. https://doi.org/10.4171/dm/780.'
ieee: 'J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy:
Spectral bands, edges and cusps,” Documenta Mathematica, vol. 25. EMS Press,
pp. 1421–1539, 2020.'
ista: 'Alt J, Erdös L, Krüger TH. 2020. The Dyson equation with linear self-energy:
Spectral bands, edges and cusps. Documenta Mathematica. 25, 1421–1539.'
mla: 'Alt, Johannes, et al. “The Dyson Equation with Linear Self-Energy: Spectral
Bands, Edges and Cusps.” Documenta Mathematica, vol. 25, EMS Press, 2020,
pp. 1421–539, doi:10.4171/dm/780.'
short: J. Alt, L. Erdös, T.H. Krüger, Documenta Mathematica 25 (2020) 1421–1539.
date_created: 2023-12-18T10:37:43Z
date_published: 2020-09-01T00:00:00Z
date_updated: 2023-12-18T10:46:09Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.4171/dm/780
external_id:
arxiv:
- '1804.07752'
file:
- access_level: open_access
checksum: 12aacc1d63b852ff9a51c1f6b218d4a6
content_type: application/pdf
creator: dernst
date_created: 2023-12-18T10:42:32Z
date_updated: 2023-12-18T10:42:32Z
file_id: '14695'
file_name: 2020_DocumentaMathematica_Alt.pdf
file_size: 1374708
relation: main_file
success: 1
file_date_updated: 2023-12-18T10:42:32Z
has_accepted_license: '1'
intvolume: ' 25'
keyword:
- General Mathematics
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 1421-1539
publication: Documenta Mathematica
publication_identifier:
eissn:
- 1431-0643
issn:
- 1431-0635
publication_status: published
publisher: EMS Press
quality_controlled: '1'
related_material:
record:
- id: '6183'
relation: earlier_version
status: public
status: public
title: 'The Dyson equation with linear self-energy: Spectral bands, edges and cusps'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 25
year: '2020'
...
---
_id: '6184'
abstract:
- lang: eng
text: We prove edge universality for a general class of correlated real symmetric
or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also
applies to internal edges of the self-consistent density of states. In particular,
we establish a strong form of band rigidity which excludes mismatches between
location and label of eigenvalues close to internal edges in these general models.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Johannes
full_name: Alt, Johannes
id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87
last_name: Alt
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: 'Alt J, Erdös L, Krüger TH, Schröder DJ. Correlated random matrices: Band rigidity
and edge universality. Annals of Probability. 2020;48(2):963-1001. doi:10.1214/19-AOP1379'
apa: 'Alt, J., Erdös, L., Krüger, T. H., & Schröder, D. J. (2020). Correlated
random matrices: Band rigidity and edge universality. Annals of Probability.
Institute of Mathematical Statistics. https://doi.org/10.1214/19-AOP1379'
chicago: 'Alt, Johannes, László Erdös, Torben H Krüger, and Dominik J Schröder.
“Correlated Random Matrices: Band Rigidity and Edge Universality.” Annals of
Probability. Institute of Mathematical Statistics, 2020. https://doi.org/10.1214/19-AOP1379.'
ieee: 'J. Alt, L. Erdös, T. H. Krüger, and D. J. Schröder, “Correlated random matrices:
Band rigidity and edge universality,” Annals of Probability, vol. 48, no.
2. Institute of Mathematical Statistics, pp. 963–1001, 2020.'
ista: 'Alt J, Erdös L, Krüger TH, Schröder DJ. 2020. Correlated random matrices:
Band rigidity and edge universality. Annals of Probability. 48(2), 963–1001.'
mla: 'Alt, Johannes, et al. “Correlated Random Matrices: Band Rigidity and Edge
Universality.” Annals of Probability, vol. 48, no. 2, Institute of Mathematical
Statistics, 2020, pp. 963–1001, doi:10.1214/19-AOP1379.'
short: J. Alt, L. Erdös, T.H. Krüger, D.J. Schröder, Annals of Probability 48 (2020)
963–1001.
date_created: 2019-03-28T09:20:08Z
date_published: 2020-03-01T00:00:00Z
date_updated: 2024-02-22T14:34:33Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/19-AOP1379
ec_funded: 1
external_id:
arxiv:
- '1804.07744'
isi:
- '000528269100013'
intvolume: ' 48'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1804.07744
month: '03'
oa: 1
oa_version: Preprint
page: 963-1001
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Annals of Probability
publication_identifier:
issn:
- 0091-1798
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
related_material:
record:
- id: '149'
relation: dissertation_contains
status: public
- id: '6179'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: 'Correlated random matrices: Band rigidity and edge universality'
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 48
year: '2020'
...
---
_id: '6185'
abstract:
- lang: eng
text: For complex Wigner-type matrices, i.e. Hermitian random matrices with independent,
not necessarily identically distributed entries above the diagonal, we show that
at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue
statistics are universal and form a Pearcey process. Since the density of states
typically exhibits only square root or cubic root cusp singularities, our work
complements previous results on the bulk and edge universality and it thus completes
the resolution of the Wigner–Dyson–Mehta universality conjecture for the last
remaining universality type in the complex Hermitian class. Our analysis holds
not only for exact cusps, but approximate cusps as well, where an extended Pearcey
process emerges. As a main technical ingredient we prove an optimal local law
at the cusp for both symmetry classes. This result is also the key input in the
companion paper (Cipolloni et al. in Pure Appl Anal, 2018. arXiv:1811.04055) where
the cusp universality for real symmetric Wigner-type matrices is proven. The novel
cusp fluctuation mechanism is also essential for the recent results on the spectral
radius of non-Hermitian random matrices (Alt et al. in Spectral radius of random
matrices with independent entries, 2019. arXiv:1907.13631), and the non-Hermitian
edge universality (Cipolloni et al. in Edge universality for non-Hermitian random
matrices, 2019. arXiv:1908.00969).
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria). The authors are very grateful to Johannes Alt for numerous discussions
on the Dyson equation and for his invaluable help in adjusting [10] to the needs
of the present work.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: 'Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices I:
Local law and the complex Hermitian case. Communications in Mathematical Physics.
2020;378:1203-1278. doi:10.1007/s00220-019-03657-4'
apa: 'Erdös, L., Krüger, T. H., & Schröder, D. J. (2020). Cusp universality
for random matrices I: Local law and the complex Hermitian case. Communications
in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-019-03657-4'
chicago: 'Erdös, László, Torben H Krüger, and Dominik J Schröder. “Cusp Universality
for Random Matrices I: Local Law and the Complex Hermitian Case.” Communications
in Mathematical Physics. Springer Nature, 2020. https://doi.org/10.1007/s00220-019-03657-4.'
ieee: 'L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random
matrices I: Local law and the complex Hermitian case,” Communications in Mathematical
Physics, vol. 378. Springer Nature, pp. 1203–1278, 2020.'
ista: 'Erdös L, Krüger TH, Schröder DJ. 2020. Cusp universality for random matrices
I: Local law and the complex Hermitian case. Communications in Mathematical Physics.
378, 1203–1278.'
mla: 'Erdös, László, et al. “Cusp Universality for Random Matrices I: Local Law
and the Complex Hermitian Case.” Communications in Mathematical Physics,
vol. 378, Springer Nature, 2020, pp. 1203–78, doi:10.1007/s00220-019-03657-4.'
short: L. Erdös, T.H. Krüger, D.J. Schröder, Communications in Mathematical Physics
378 (2020) 1203–1278.
date_created: 2019-03-28T10:21:15Z
date_published: 2020-09-01T00:00:00Z
date_updated: 2023-09-07T12:54:12Z
day: '01'
ddc:
- '530'
- '510'
department:
- _id: LaEr
doi: 10.1007/s00220-019-03657-4
ec_funded: 1
external_id:
arxiv:
- '1809.03971'
isi:
- '000529483000001'
file:
- access_level: open_access
checksum: c3a683e2afdcea27afa6880b01e53dc2
content_type: application/pdf
creator: dernst
date_created: 2020-11-18T11:14:37Z
date_updated: 2020-11-18T11:14:37Z
file_id: '8771'
file_name: 2020_CommMathPhysics_Erdoes.pdf
file_size: 2904574
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file_date_updated: 2020-11-18T11:14:37Z
has_accepted_license: '1'
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language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 1203-1278
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '6179'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: 'Cusp universality for random matrices I: Local law and the complex Hermitian
case'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 378
year: '2020'
...
---
_id: '6182'
abstract:
- lang: eng
text: "We consider large random matrices with a general slowly decaying correlation
among its entries. We prove universality of the local eigenvalue statistics and
optimal local laws for the resolvent away from the spectral edges, generalizing
the recent result of Ajanki et al. [‘Stability of the matrix Dyson equation and
random matrices with correlations’, Probab. Theory Related Fields 173(1–2) (2019),
293–373] to allow slow correlation decay and arbitrary expectation. The main novel
tool is\r\na systematic diagrammatic control of a multivariate cumulant expansion."
article_number: e8
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: Erdös L, Krüger TH, Schröder DJ. Random matrices with slow correlation decay.
Forum of Mathematics, Sigma. 2019;7. doi:10.1017/fms.2019.2
apa: Erdös, L., Krüger, T. H., & Schröder, D. J. (2019). Random matrices with
slow correlation decay. Forum of Mathematics, Sigma. Cambridge University
Press. https://doi.org/10.1017/fms.2019.2
chicago: Erdös, László, Torben H Krüger, and Dominik J Schröder. “Random Matrices
with Slow Correlation Decay.” Forum of Mathematics, Sigma. Cambridge University
Press, 2019. https://doi.org/10.1017/fms.2019.2.
ieee: L. Erdös, T. H. Krüger, and D. J. Schröder, “Random matrices with slow correlation
decay,” Forum of Mathematics, Sigma, vol. 7. Cambridge University Press,
2019.
ista: Erdös L, Krüger TH, Schröder DJ. 2019. Random matrices with slow correlation
decay. Forum of Mathematics, Sigma. 7, e8.
mla: Erdös, László, et al. “Random Matrices with Slow Correlation Decay.” Forum
of Mathematics, Sigma, vol. 7, e8, Cambridge University Press, 2019, doi:10.1017/fms.2019.2.
short: L. Erdös, T.H. Krüger, D.J. Schröder, Forum of Mathematics, Sigma 7 (2019).
date_created: 2019-03-28T09:05:23Z
date_published: 2019-03-26T00:00:00Z
date_updated: 2023-09-07T12:54:12Z
day: '26'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1017/fms.2019.2
ec_funded: 1
external_id:
arxiv:
- '1705.10661'
isi:
- '000488847100001'
file:
- access_level: open_access
checksum: 933a472568221c73b2c3ce8c87bf6d15
content_type: application/pdf
creator: dernst
date_created: 2019-09-17T14:24:13Z
date_updated: 2020-07-14T12:47:22Z
file_id: '6883'
file_name: 2019_Forum_Erdoes.pdf
file_size: 1520344
relation: main_file
file_date_updated: 2020-07-14T12:47:22Z
has_accepted_license: '1'
intvolume: ' 7'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Forum of Mathematics, Sigma
publication_identifier:
eissn:
- '20505094'
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
related_material:
record:
- id: '6179'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Random matrices with slow correlation decay
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 7
year: '2019'
...
---
_id: '6186'
abstract:
- lang: eng
text: "We prove that the local eigenvalue statistics of real symmetric Wigner-type\r\nmatrices
near the cusp points of the eigenvalue density are universal. Together\r\nwith
the companion paper [arXiv:1809.03971], which proves the same result for\r\nthe
complex Hermitian symmetry class, this completes the last remaining case of\r\nthe
Wigner-Dyson-Mehta universality conjecture after bulk and edge\r\nuniversalities
have been established in the last years. We extend the recent\r\nDyson Brownian
motion analysis at the edge [arXiv:1712.03881] to the cusp\r\nregime using the
optimal local law from [arXiv:1809.03971] and the accurate\r\nlocal shape analysis
of the density from [arXiv:1506.05095, arXiv:1804.07752].\r\nWe also present a
PDE-based method to improve the estimate on eigenvalue\r\nrigidity via the maximum
principle of the heat flow related to the Dyson\r\nBrownian motion."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: 'Cipolloni G, Erdös L, Krüger TH, Schröder DJ. Cusp universality for random
matrices, II: The real symmetric case. Pure and Applied Analysis . 2019;1(4):615–707.
doi:10.2140/paa.2019.1.615'
apa: 'Cipolloni, G., Erdös, L., Krüger, T. H., & Schröder, D. J. (2019). Cusp
universality for random matrices, II: The real symmetric case. Pure and Applied
Analysis . MSP. https://doi.org/10.2140/paa.2019.1.615'
chicago: 'Cipolloni, Giorgio, László Erdös, Torben H Krüger, and Dominik J Schröder.
“Cusp Universality for Random Matrices, II: The Real Symmetric Case.” Pure
and Applied Analysis . MSP, 2019. https://doi.org/10.2140/paa.2019.1.615.'
ieee: 'G. Cipolloni, L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality
for random matrices, II: The real symmetric case,” Pure and Applied Analysis
, vol. 1, no. 4. MSP, pp. 615–707, 2019.'
ista: 'Cipolloni G, Erdös L, Krüger TH, Schröder DJ. 2019. Cusp universality for
random matrices, II: The real symmetric case. Pure and Applied Analysis . 1(4),
615–707.'
mla: 'Cipolloni, Giorgio, et al. “Cusp Universality for Random Matrices, II: The
Real Symmetric Case.” Pure and Applied Analysis , vol. 1, no. 4, MSP, 2019,
pp. 615–707, doi:10.2140/paa.2019.1.615.'
short: G. Cipolloni, L. Erdös, T.H. Krüger, D.J. Schröder, Pure and Applied Analysis 1
(2019) 615–707.
date_created: 2019-03-28T10:21:17Z
date_published: 2019-10-12T00:00:00Z
date_updated: 2023-09-07T12:54:12Z
day: '12'
department:
- _id: LaEr
doi: 10.2140/paa.2019.1.615
ec_funded: 1
external_id:
arxiv:
- '1811.04055'
intvolume: ' 1'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1811.04055
month: '10'
oa: 1
oa_version: Preprint
page: 615–707
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: 'Pure and Applied Analysis '
publication_identifier:
eissn:
- 2578-5885
issn:
- 2578-5893
publication_status: published
publisher: MSP
quality_controlled: '1'
related_material:
record:
- id: '6179'
relation: dissertation_contains
status: public
status: public
title: 'Cusp universality for random matrices, II: The real symmetric case'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 1
year: '2019'
...
---
_id: '6240'
abstract:
- lang: eng
text: For a general class of large non-Hermitian random block matrices X we prove
that there are no eigenvalues away from a deterministic set with very high probability.
This set is obtained from the Dyson equation of the Hermitization of X as the
self-consistent approximation of the pseudospectrum. We demonstrate that the analysis
of the matrix Dyson equation from (Probab. Theory Related Fields (2018)) offers
a unified treatment of many structured matrix ensembles.
article_processing_charge: No
arxiv: 1
author:
- first_name: Johannes
full_name: Alt, Johannes
id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87
last_name: Alt
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- first_name: Yuriy
full_name: Nemish, Yuriy
id: 4D902E6A-F248-11E8-B48F-1D18A9856A87
last_name: Nemish
orcid: 0000-0002-7327-856X
citation:
ama: Alt J, Erdös L, Krüger TH, Nemish Y. Location of the spectrum of Kronecker
random matrices. Annales de l’institut Henri Poincare. 2019;55(2):661-696.
doi:10.1214/18-AIHP894
apa: Alt, J., Erdös, L., Krüger, T. H., & Nemish, Y. (2019). Location of the
spectrum of Kronecker random matrices. Annales de l’institut Henri Poincare.
Institut Henri Poincaré. https://doi.org/10.1214/18-AIHP894
chicago: Alt, Johannes, László Erdös, Torben H Krüger, and Yuriy Nemish. “Location
of the Spectrum of Kronecker Random Matrices.” Annales de l’institut Henri
Poincare. Institut Henri Poincaré, 2019. https://doi.org/10.1214/18-AIHP894.
ieee: J. Alt, L. Erdös, T. H. Krüger, and Y. Nemish, “Location of the spectrum of
Kronecker random matrices,” Annales de l’institut Henri Poincare, vol.
55, no. 2. Institut Henri Poincaré, pp. 661–696, 2019.
ista: Alt J, Erdös L, Krüger TH, Nemish Y. 2019. Location of the spectrum of Kronecker
random matrices. Annales de l’institut Henri Poincare. 55(2), 661–696.
mla: Alt, Johannes, et al. “Location of the Spectrum of Kronecker Random Matrices.”
Annales de l’institut Henri Poincare, vol. 55, no. 2, Institut Henri Poincaré,
2019, pp. 661–96, doi:10.1214/18-AIHP894.
short: J. Alt, L. Erdös, T.H. Krüger, Y. Nemish, Annales de l’institut Henri Poincare
55 (2019) 661–696.
date_created: 2019-04-08T14:05:04Z
date_published: 2019-05-01T00:00:00Z
date_updated: 2023-10-17T12:20:20Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/18-AIHP894
ec_funded: 1
external_id:
arxiv:
- '1706.08343'
isi:
- '000467793600003'
intvolume: ' 55'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1706.08343
month: '05'
oa: 1
oa_version: Preprint
page: 661-696
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Annales de l'institut Henri Poincare
publication_identifier:
issn:
- 0246-0203
publication_status: published
publisher: Institut Henri Poincaré
quality_controlled: '1'
related_material:
record:
- id: '149'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Location of the spectrum of Kronecker random matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 55
year: '2019'
...
---
_id: '429'
abstract:
- lang: eng
text: We consider real symmetric or complex hermitian random matrices with correlated
entries. We prove local laws for the resolvent and universality of the local eigenvalue
statistics in the bulk of the spectrum. The correlations have fast decay but are
otherwise of general form. The key novelty is the detailed stability analysis
of the corresponding matrix valued Dyson equation whose solution is the deterministic
limit of the resolvent.
acknowledgement: "Open access funding provided by Institute of Science and Technology
(IST Austria).\r\n"
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Oskari H
full_name: Ajanki, Oskari H
id: 36F2FB7E-F248-11E8-B48F-1D18A9856A87
last_name: Ajanki
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
citation:
ama: Ajanki OH, Erdös L, Krüger TH. Stability of the matrix Dyson equation and random
matrices with correlations. Probability Theory and Related Fields. 2019;173(1-2):293–373.
doi:10.1007/s00440-018-0835-z
apa: Ajanki, O. H., Erdös, L., & Krüger, T. H. (2019). Stability of the matrix
Dyson equation and random matrices with correlations. Probability Theory and
Related Fields. Springer. https://doi.org/10.1007/s00440-018-0835-z
chicago: Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Stability of the
Matrix Dyson Equation and Random Matrices with Correlations.” Probability Theory
and Related Fields. Springer, 2019. https://doi.org/10.1007/s00440-018-0835-z.
ieee: O. H. Ajanki, L. Erdös, and T. H. Krüger, “Stability of the matrix Dyson equation
and random matrices with correlations,” Probability Theory and Related Fields,
vol. 173, no. 1–2. Springer, pp. 293–373, 2019.
ista: Ajanki OH, Erdös L, Krüger TH. 2019. Stability of the matrix Dyson equation
and random matrices with correlations. Probability Theory and Related Fields.
173(1–2), 293–373.
mla: Ajanki, Oskari H., et al. “Stability of the Matrix Dyson Equation and Random
Matrices with Correlations.” Probability Theory and Related Fields, vol.
173, no. 1–2, Springer, 2019, pp. 293–373, doi:10.1007/s00440-018-0835-z.
short: O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields
173 (2019) 293–373.
date_created: 2018-12-11T11:46:25Z
date_published: 2019-02-01T00:00:00Z
date_updated: 2023-08-24T14:39:00Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00440-018-0835-z
ec_funded: 1
external_id:
isi:
- '000459396500007'
file:
- access_level: open_access
checksum: f9354fa5c71f9edd17132588f0dc7d01
content_type: application/pdf
creator: dernst
date_created: 2018-12-17T16:12:08Z
date_updated: 2020-07-14T12:46:26Z
file_id: '5720'
file_name: 2018_ProbTheory_Ajanki.pdf
file_size: 1201840
relation: main_file
file_date_updated: 2020-07-14T12:46:26Z
has_accepted_license: '1'
intvolume: ' 173'
isi: 1
issue: 1-2
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 293–373
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Probability Theory and Related Fields
publication_identifier:
eissn:
- '14322064'
issn:
- '01788051'
publication_status: published
publisher: Springer
publist_id: '7394'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Stability of the matrix Dyson equation and random matrices with correlations
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 173
year: '2019'
...
---
_id: '181'
abstract:
- lang: eng
text: We consider large random matrices X with centered, independent entries but
possibly di erent variances. We compute the normalized trace of f(X)g(X∗) for
f, g functions analytic on the spectrum of X. We use these results to compute
the long time asymptotics for systems of coupled di erential equations with random
coe cients. We show that when the coupling is critical, the norm squared of the
solution decays like t−1/2.
acknowledgement: The work of the second author was also partially supported by the
Hausdorff Center of Mathematics.
article_processing_charge: No
arxiv: 1
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- first_name: David T
full_name: Renfrew, David T
id: 4845BF6A-F248-11E8-B48F-1D18A9856A87
last_name: Renfrew
orcid: 0000-0003-3493-121X
citation:
ama: Erdös L, Krüger TH, Renfrew DT. Power law decay for systems of randomly coupled
differential equations. SIAM Journal on Mathematical Analysis. 2018;50(3):3271-3290.
doi:10.1137/17M1143125
apa: Erdös, L., Krüger, T. H., & Renfrew, D. T. (2018). Power law decay for
systems of randomly coupled differential equations. SIAM Journal on Mathematical
Analysis. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/17M1143125
chicago: Erdös, László, Torben H Krüger, and David T Renfrew. “Power Law Decay for
Systems of Randomly Coupled Differential Equations.” SIAM Journal on Mathematical
Analysis. Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/17M1143125.
ieee: L. Erdös, T. H. Krüger, and D. T. Renfrew, “Power law decay for systems of
randomly coupled differential equations,” SIAM Journal on Mathematical Analysis,
vol. 50, no. 3. Society for Industrial and Applied Mathematics , pp. 3271–3290,
2018.
ista: Erdös L, Krüger TH, Renfrew DT. 2018. Power law decay for systems of randomly
coupled differential equations. SIAM Journal on Mathematical Analysis. 50(3),
3271–3290.
mla: Erdös, László, et al. “Power Law Decay for Systems of Randomly Coupled Differential
Equations.” SIAM Journal on Mathematical Analysis, vol. 50, no. 3, Society
for Industrial and Applied Mathematics , 2018, pp. 3271–90, doi:10.1137/17M1143125.
short: L. Erdös, T.H. Krüger, D.T. Renfrew, SIAM Journal on Mathematical Analysis
50 (2018) 3271–3290.
date_created: 2018-12-11T11:45:03Z
date_published: 2018-01-01T00:00:00Z
date_updated: 2023-09-15T12:05:52Z
day: '01'
department:
- _id: LaEr
doi: 10.1137/17M1143125
ec_funded: 1
external_id:
arxiv:
- '1708.01546'
isi:
- '000437018500032'
intvolume: ' 50'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1708.01546
month: '01'
oa: 1
oa_version: Published Version
page: 3271 - 3290
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: 258F40A4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: M02080
name: Structured Non-Hermitian Random Matrices
publication: SIAM Journal on Mathematical Analysis
publication_status: published
publisher: 'Society for Industrial and Applied Mathematics '
publist_id: '7740'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Power law decay for systems of randomly coupled differential equations
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 50
year: '2018'
...
---
_id: '566'
abstract:
- lang: eng
text: "We consider large random matrices X with centered, independent entries which
have comparable but not necessarily identical variances. Girko's circular law
asserts that the spectrum is supported in a disk and in case of identical variances,
the limiting density is uniform. In this special case, the local circular law
by Bourgade et. al. [11,12] shows that the empirical density converges even locally
on scales slightly above the typical eigenvalue spacing. In the general case,
the limiting density is typically inhomogeneous and it is obtained via solving
a system of deterministic equations. Our main result is the local inhomogeneous
circular law in the bulk spectrum on the optimal scale for a general variance
profile of the entries of X. \r\n\r\n"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Johannes
full_name: Alt, Johannes
id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87
last_name: Alt
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
citation:
ama: Alt J, Erdös L, Krüger TH. Local inhomogeneous circular law. Annals Applied
Probability . 2018;28(1):148-203. doi:10.1214/17-AAP1302
apa: Alt, J., Erdös, L., & Krüger, T. H. (2018). Local inhomogeneous circular
law. Annals Applied Probability . Institute of Mathematical Statistics.
https://doi.org/10.1214/17-AAP1302
chicago: Alt, Johannes, László Erdös, and Torben H Krüger. “Local Inhomogeneous
Circular Law.” Annals Applied Probability . Institute of Mathematical Statistics,
2018. https://doi.org/10.1214/17-AAP1302.
ieee: J. Alt, L. Erdös, and T. H. Krüger, “Local inhomogeneous circular law,” Annals
Applied Probability , vol. 28, no. 1. Institute of Mathematical Statistics,
pp. 148–203, 2018.
ista: Alt J, Erdös L, Krüger TH. 2018. Local inhomogeneous circular law. Annals
Applied Probability . 28(1), 148–203.
mla: Alt, Johannes, et al. “Local Inhomogeneous Circular Law.” Annals Applied
Probability , vol. 28, no. 1, Institute of Mathematical Statistics, 2018,
pp. 148–203, doi:10.1214/17-AAP1302.
short: J. Alt, L. Erdös, T.H. Krüger, Annals Applied Probability 28 (2018) 148–203.
date_created: 2018-12-11T11:47:13Z
date_published: 2018-03-03T00:00:00Z
date_updated: 2023-09-13T08:47:52Z
day: '03'
department:
- _id: LaEr
doi: 10.1214/17-AAP1302
ec_funded: 1
external_id:
arxiv:
- '1612.07776 '
isi:
- '000431721800005'
intvolume: ' 28'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: 'https://arxiv.org/abs/1612.07776 '
month: '03'
oa: 1
oa_version: Preprint
page: 148-203
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: 'Annals Applied Probability '
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
related_material:
record:
- id: '149'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Local inhomogeneous circular law
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 28
year: '2018'
...
---
_id: '6183'
abstract:
- lang: eng
text: "We study the unique solution $m$ of the Dyson equation \\[ -m(z)^{-1} = z
- a\r\n+ S[m(z)] \\] on a von Neumann algebra $\\mathcal{A}$ with the constraint\r\n$\\mathrm{Im}\\,m\\geq
0$. Here, $z$ lies in the complex upper half-plane, $a$ is\r\na self-adjoint element
of $\\mathcal{A}$ and $S$ is a positivity-preserving\r\nlinear operator on $\\mathcal{A}$.
We show that $m$ is the Stieltjes transform\r\nof a compactly supported $\\mathcal{A}$-valued
measure on $\\mathbb{R}$. Under\r\nsuitable assumptions, we establish that this
measure has a uniformly\r\n$1/3$-H\\\"{o}lder continuous density with respect
to the Lebesgue measure, which\r\nis supported on finitely many intervals, called
bands. In fact, the density is\r\nanalytic inside the bands with a square-root
growth at the edges and internal\r\ncubic root cusps whenever the gap between
two bands vanishes. The shape of\r\nthese singularities is universal and no other
singularity may occur. We give a\r\nprecise asymptotic description of $m$ near
the singular points. These\r\nasymptotics generalize the analysis at the regular
edges given in the companion\r\npaper on the Tracy-Widom universality for the
edge eigenvalue statistics for\r\ncorrelated random matrices [arXiv:1804.07744]
and they play a key role in the\r\nproof of the Pearcey universality at the cusp
for Wigner-type matrices\r\n[arXiv:1809.03971,arXiv:1811.04055]. We also extend
the finite dimensional band\r\nmass formula from [arXiv:1804.07744] to the von
Neumann algebra setting by\r\nshowing that the spectral mass of the bands is topologically
rigid under\r\ndeformations and we conclude that these masses are quantized in
some important\r\ncases."
article_number: '1804.07752'
article_processing_charge: No
arxiv: 1
author:
- first_name: Johannes
full_name: Alt, Johannes
id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87
last_name: Alt
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
citation:
ama: 'Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral
bands, edges and cusps. arXiv.'
apa: 'Alt, J., Erdös, L., & Krüger, T. H. (n.d.). The Dyson equation with linear
self-energy: Spectral bands, edges and cusps. arXiv.'
chicago: 'Alt, Johannes, László Erdös, and Torben H Krüger. “The Dyson Equation
with Linear Self-Energy: Spectral Bands, Edges and Cusps.” ArXiv, n.d.'
ieee: 'J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy:
Spectral bands, edges and cusps,” arXiv. .'
ista: 'Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral
bands, edges and cusps. arXiv, 1804.07752.'
mla: 'Alt, Johannes, et al. “The Dyson Equation with Linear Self-Energy: Spectral
Bands, Edges and Cusps.” ArXiv, 1804.07752.'
short: J. Alt, L. Erdös, T.H. Krüger, ArXiv (n.d.).
date_created: 2019-03-28T09:20:06Z
date_published: 2018-04-20T00:00:00Z
date_updated: 2023-12-18T10:46:08Z
day: '20'
department:
- _id: LaEr
external_id:
arxiv:
- '1804.07752'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1804.07752
month: '04'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: submitted
related_material:
record:
- id: '149'
relation: dissertation_contains
status: public
- id: '14694'
relation: later_version
status: public
status: public
title: 'The Dyson equation with linear self-energy: Spectral bands, edges and cusps'
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2018'
...
---
_id: '721'
abstract:
- lang: eng
text: 'Let S be a positivity-preserving symmetric linear operator acting on bounded
functions. The nonlinear equation -1/m=z+Sm with a parameter z in the complex
upper half-plane ℍ has a unique solution m with values in ℍ. We show that the
z-dependence of this solution can be represented as the Stieltjes transforms of
a family of probability measures v on ℝ. Under suitable conditions on S, we show
that v has a real analytic density apart from finitely many algebraic singularities
of degree at most 3. Our motivation comes from large random matrices. The solution
m determines the density of eigenvalues of two prominent matrix ensembles: (i)
matrices with centered independent entries whose variances are given by S and
(ii) matrices with correlated entries with a translation-invariant correlation
structure. Our analysis shows that the limiting eigenvalue density has only square
root singularities or cubic root cusps; no other singularities occur.'
author:
- first_name: Oskari H
full_name: Ajanki, Oskari H
id: 36F2FB7E-F248-11E8-B48F-1D18A9856A87
last_name: Ajanki
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
citation:
ama: Ajanki OH, Krüger TH, Erdös L. Singularities of solutions to quadratic vector
equations on the complex upper half plane. Communications on Pure and Applied
Mathematics. 2017;70(9):1672-1705. doi:10.1002/cpa.21639
apa: Ajanki, O. H., Krüger, T. H., & Erdös, L. (2017). Singularities of solutions
to quadratic vector equations on the complex upper half plane. Communications
on Pure and Applied Mathematics. Wiley-Blackwell. https://doi.org/10.1002/cpa.21639
chicago: Ajanki, Oskari H, Torben H Krüger, and László Erdös. “Singularities of
Solutions to Quadratic Vector Equations on the Complex Upper Half Plane.” Communications
on Pure and Applied Mathematics. Wiley-Blackwell, 2017. https://doi.org/10.1002/cpa.21639.
ieee: O. H. Ajanki, T. H. Krüger, and L. Erdös, “Singularities of solutions to quadratic
vector equations on the complex upper half plane,” Communications on Pure and
Applied Mathematics, vol. 70, no. 9. Wiley-Blackwell, pp. 1672–1705, 2017.
ista: Ajanki OH, Krüger TH, Erdös L. 2017. Singularities of solutions to quadratic
vector equations on the complex upper half plane. Communications on Pure and Applied
Mathematics. 70(9), 1672–1705.
mla: Ajanki, Oskari H., et al. “Singularities of Solutions to Quadratic Vector Equations
on the Complex Upper Half Plane.” Communications on Pure and Applied Mathematics,
vol. 70, no. 9, Wiley-Blackwell, 2017, pp. 1672–705, doi:10.1002/cpa.21639.
short: O.H. Ajanki, T.H. Krüger, L. Erdös, Communications on Pure and Applied Mathematics
70 (2017) 1672–1705.
date_created: 2018-12-11T11:48:08Z
date_published: 2017-09-01T00:00:00Z
date_updated: 2021-01-12T08:12:24Z
day: '01'
department:
- _id: LaEr
doi: 10.1002/cpa.21639
ec_funded: 1
intvolume: ' 70'
issue: '9'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1512.03703
month: '09'
oa: 1
oa_version: Submitted Version
page: 1672 - 1705
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Communications on Pure and Applied Mathematics
publication_identifier:
issn:
- '00103640'
publication_status: published
publisher: Wiley-Blackwell
publist_id: '6959'
quality_controlled: '1'
scopus_import: 1
status: public
title: Singularities of solutions to quadratic vector equations on the complex upper
half plane
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 70
year: '2017'
...
---
_id: '1337'
abstract:
- lang: eng
text: We consider the local eigenvalue distribution of large self-adjoint N×N random
matrices H=H∗ with centered independent entries. In contrast to previous works
the matrix of variances sij=\mathbbmE|hij|2 is not assumed to be stochastic. Hence
the density of states is not the Wigner semicircle law. Its possible shapes are
described in the companion paper (Ajanki et al. in Quadratic Vector Equations
on the Complex Upper Half Plane. arXiv:1506.05095). We show that as N grows, the
resolvent, G(z)=(H−z)−1, converges to a diagonal matrix, diag(m(z)), where m(z)=(m1(z),…,mN(z))
solves the vector equation −1/mi(z)=z+∑jsijmj(z) that has been analyzed in Ajanki
et al. (Quadratic Vector Equations on the Complex Upper Half Plane. arXiv:1506.05095).
We prove a local law down to the smallest spectral resolution scale, and bulk
universality for both real symmetric and complex hermitian symmetry classes.
acknowledgement: 'Open access funding provided by Institute of Science and Technology
(IST Austria). '
article_processing_charge: Yes (via OA deal)
author:
- first_name: Oskari H
full_name: Ajanki, Oskari H
id: 36F2FB7E-F248-11E8-B48F-1D18A9856A87
last_name: Ajanki
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
citation:
ama: Ajanki OH, Erdös L, Krüger TH. Universality for general Wigner-type matrices.
Probability Theory and Related Fields. 2017;169(3-4):667-727. doi:10.1007/s00440-016-0740-2
apa: Ajanki, O. H., Erdös, L., & Krüger, T. H. (2017). Universality for general
Wigner-type matrices. Probability Theory and Related Fields. Springer.
https://doi.org/10.1007/s00440-016-0740-2
chicago: Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Universality for
General Wigner-Type Matrices.” Probability Theory and Related Fields. Springer,
2017. https://doi.org/10.1007/s00440-016-0740-2.
ieee: O. H. Ajanki, L. Erdös, and T. H. Krüger, “Universality for general Wigner-type
matrices,” Probability Theory and Related Fields, vol. 169, no. 3–4. Springer,
pp. 667–727, 2017.
ista: Ajanki OH, Erdös L, Krüger TH. 2017. Universality for general Wigner-type
matrices. Probability Theory and Related Fields. 169(3–4), 667–727.
mla: Ajanki, Oskari H., et al. “Universality for General Wigner-Type Matrices.”
Probability Theory and Related Fields, vol. 169, no. 3–4, Springer, 2017,
pp. 667–727, doi:10.1007/s00440-016-0740-2.
short: O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields
169 (2017) 667–727.
date_created: 2018-12-11T11:51:27Z
date_published: 2017-12-01T00:00:00Z
date_updated: 2023-09-20T11:14:17Z
day: '01'
ddc:
- '510'
- '530'
department:
- _id: LaEr
doi: 10.1007/s00440-016-0740-2
ec_funded: 1
external_id:
isi:
- '000414358400002'
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- access_level: open_access
checksum: 29f5a72c3f91e408aeb9e78344973803
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creator: system
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oa: 1
oa_version: Published Version
page: 667 - 727
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call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Probability Theory and Related Fields
publication_identifier:
issn:
- '01788051'
publication_status: published
publisher: Springer
publist_id: '5930'
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quality_controlled: '1'
scopus_import: '1'
status: public
title: Universality for general Wigner-type matrices
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 169
year: '2017'
...
---
_id: '1010'
abstract:
- lang: eng
text: 'We prove a local law in the bulk of the spectrum for random Gram matrices
XX∗, a generalization of sample covariance matrices, where X is a large matrix
with independent, centered entries with arbitrary variances. The limiting eigenvalue
density that generalizes the Marchenko-Pastur law is determined by solving a system
of nonlinear equations. Our entrywise and averaged local laws are on the optimal
scale with the optimal error bounds. They hold both in the square case (hard edge)
and in the properly rectangular case (soft edge). In the latter case we also establish
a macroscopic gap away from zero in the spectrum of XX∗. '
article_number: '25'
article_processing_charge: No
arxiv: 1
author:
- first_name: Johannes
full_name: Alt, Johannes
id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87
last_name: Alt
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
citation:
ama: Alt J, Erdös L, Krüger TH. Local law for random Gram matrices. Electronic
Journal of Probability. 2017;22. doi:10.1214/17-EJP42
apa: Alt, J., Erdös, L., & Krüger, T. H. (2017). Local law for random Gram matrices.
Electronic Journal of Probability. Institute of Mathematical Statistics.
https://doi.org/10.1214/17-EJP42
chicago: Alt, Johannes, László Erdös, and Torben H Krüger. “Local Law for Random
Gram Matrices.” Electronic Journal of Probability. Institute of Mathematical
Statistics, 2017. https://doi.org/10.1214/17-EJP42.
ieee: J. Alt, L. Erdös, and T. H. Krüger, “Local law for random Gram matrices,”
Electronic Journal of Probability, vol. 22. Institute of Mathematical Statistics,
2017.
ista: Alt J, Erdös L, Krüger TH. 2017. Local law for random Gram matrices. Electronic
Journal of Probability. 22, 25.
mla: Alt, Johannes, et al. “Local Law for Random Gram Matrices.” Electronic Journal
of Probability, vol. 22, 25, Institute of Mathematical Statistics, 2017, doi:10.1214/17-EJP42.
short: J. Alt, L. Erdös, T.H. Krüger, Electronic Journal of Probability 22 (2017).
date_created: 2018-12-11T11:49:40Z
date_published: 2017-03-08T00:00:00Z
date_updated: 2023-09-22T09:45:23Z
day: '08'
ddc:
- '510'
- '539'
department:
- _id: LaEr
doi: 10.1214/17-EJP42
ec_funded: 1
external_id:
arxiv:
- '1606.07353'
isi:
- '000396611900025'
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language:
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month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Electronic Journal of Probability
publication_identifier:
issn:
- '10836489'
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '6386'
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quality_controlled: '1'
related_material:
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- id: '149'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Local law for random Gram matrices
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 22
year: '2017'
...
---
_id: '1489'
abstract:
- lang: eng
text: 'We prove optimal local law, bulk universality and non-trivial decay for the
off-diagonal elements of the resolvent for a class of translation invariant Gaussian
random matrix ensembles with correlated entries. '
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria). Oskari H. Ajanki was Partially supported by ERC Advanced Grant RANMAT
No. 338804, and SFB-TR 12 Grant of the German Research Council. László Erdős was
Partially supported by ERC Advanced Grant RANMAT No. 338804. Torben Krüger was Partially
supported by ERC Advanced Grant RANMAT No. 338804, and SFB-TR 12 Grant of the German
Research Council.
article_processing_charge: Yes (via OA deal)
author:
- first_name: Oskari H
full_name: Ajanki, Oskari H
id: 36F2FB7E-F248-11E8-B48F-1D18A9856A87
last_name: Ajanki
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
citation:
ama: Ajanki OH, Erdös L, Krüger TH. Local spectral statistics of Gaussian matrices
with correlated entries. Journal of Statistical Physics. 2016;163(2):280-302.
doi:10.1007/s10955-016-1479-y
apa: Ajanki, O. H., Erdös, L., & Krüger, T. H. (2016). Local spectral statistics
of Gaussian matrices with correlated entries. Journal of Statistical Physics.
Springer. https://doi.org/10.1007/s10955-016-1479-y
chicago: Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Local Spectral Statistics
of Gaussian Matrices with Correlated Entries.” Journal of Statistical Physics.
Springer, 2016. https://doi.org/10.1007/s10955-016-1479-y.
ieee: O. H. Ajanki, L. Erdös, and T. H. Krüger, “Local spectral statistics of Gaussian
matrices with correlated entries,” Journal of Statistical Physics, vol.
163, no. 2. Springer, pp. 280–302, 2016.
ista: Ajanki OH, Erdös L, Krüger TH. 2016. Local spectral statistics of Gaussian
matrices with correlated entries. Journal of Statistical Physics. 163(2), 280–302.
mla: Ajanki, Oskari H., et al. “Local Spectral Statistics of Gaussian Matrices with
Correlated Entries.” Journal of Statistical Physics, vol. 163, no. 2, Springer,
2016, pp. 280–302, doi:10.1007/s10955-016-1479-y.
short: O.H. Ajanki, L. Erdös, T.H. Krüger, Journal of Statistical Physics 163 (2016)
280–302.
date_created: 2018-12-11T11:52:19Z
date_published: 2016-04-01T00:00:00Z
date_updated: 2021-01-12T06:51:05Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s10955-016-1479-y
ec_funded: 1
file:
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checksum: 7139598dcb1cafbe6866bd2bfd732b33
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has_accepted_license: '1'
intvolume: ' 163'
issue: '2'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 280 - 302
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Journal of Statistical Physics
publication_status: published
publisher: Springer
publist_id: '5698'
pubrep_id: '516'
quality_controlled: '1'
scopus_import: 1
status: public
title: Local spectral statistics of Gaussian matrices with correlated entries
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 163
year: '2016'
...
---
_id: '1824'
abstract:
- lang: eng
text: Condensation phenomena arise through a collective behaviour of particles.
They are observed in both classical and quantum systems, ranging from the formation
of traffic jams in mass transport models to the macroscopic occupation of the
energetic ground state in ultra-cold bosonic gases (Bose-Einstein condensation).
Recently, it has been shown that a driven and dissipative system of bosons may
form multiple condensates. Which states become the condensates has, however, remained
elusive thus far. The dynamics of this condensation are described by coupled birth-death
processes, which also occur in evolutionary game theory. Here we apply concepts
from evolutionary game theory to explain the formation of multiple condensates
in such driven-dissipative bosonic systems. We show that the vanishing of relative
entropy production determines their selection. The condensation proceeds exponentially
fast, but the system never comes to rest. Instead, the occupation numbers of condensates
may oscillate, as we demonstrate for a rock-paper-scissors game of condensates.
article_number: '6977'
author:
- first_name: Johannes
full_name: Knebel, Johannes
last_name: Knebel
- first_name: Markus
full_name: Weber, Markus
last_name: Weber
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- first_name: Erwin
full_name: Frey, Erwin
last_name: Frey
citation:
ama: Knebel J, Weber M, Krüger TH, Frey E. Evolutionary games of condensates in
coupled birth-death processes. Nature Communications. 2015;6. doi:10.1038/ncomms7977
apa: Knebel, J., Weber, M., Krüger, T. H., & Frey, E. (2015). Evolutionary games
of condensates in coupled birth-death processes. Nature Communications.
Nature Publishing Group. https://doi.org/10.1038/ncomms7977
chicago: Knebel, Johannes, Markus Weber, Torben H Krüger, and Erwin Frey. “Evolutionary
Games of Condensates in Coupled Birth-Death Processes.” Nature Communications.
Nature Publishing Group, 2015. https://doi.org/10.1038/ncomms7977.
ieee: J. Knebel, M. Weber, T. H. Krüger, and E. Frey, “Evolutionary games of condensates
in coupled birth-death processes,” Nature Communications, vol. 6. Nature
Publishing Group, 2015.
ista: Knebel J, Weber M, Krüger TH, Frey E. 2015. Evolutionary games of condensates
in coupled birth-death processes. Nature Communications. 6, 6977.
mla: Knebel, Johannes, et al. “Evolutionary Games of Condensates in Coupled Birth-Death
Processes.” Nature Communications, vol. 6, 6977, Nature Publishing Group,
2015, doi:10.1038/ncomms7977.
short: J. Knebel, M. Weber, T.H. Krüger, E. Frey, Nature Communications 6 (2015).
date_created: 2018-12-11T11:54:13Z
date_published: 2015-04-24T00:00:00Z
date_updated: 2021-01-12T06:53:26Z
day: '24'
ddc:
- '530'
department:
- _id: LaEr
doi: 10.1038/ncomms7977
file:
- access_level: open_access
checksum: c4cffb5c8b245e658a34eac71a03e7cc
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:16:54Z
date_updated: 2020-07-14T12:45:17Z
file_id: '5245'
file_name: IST-2016-451-v1+1_ncomms7977.pdf
file_size: 1151501
relation: main_file
file_date_updated: 2020-07-14T12:45:17Z
has_accepted_license: '1'
intvolume: ' 6'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
publication: Nature Communications
publication_status: published
publisher: Nature Publishing Group
publist_id: '5282'
pubrep_id: '451'
quality_controlled: '1'
scopus_import: 1
status: public
title: Evolutionary games of condensates in coupled birth-death processes
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 6
year: '2015'
...
---
_id: '2179'
abstract:
- lang: eng
text: We extend the proof of the local semicircle law for generalized Wigner matrices
given in MR3068390 to the case when the matrix of variances has an eigenvalue
-1. In particular, this result provides a short proof of the optimal local Marchenko-Pastur
law at the hard edge (i.e. around zero) for sample covariance matrices X*X, where
the variances of the entries of X may vary.
author:
- first_name: Oskari H
full_name: Ajanki, Oskari H
id: 36F2FB7E-F248-11E8-B48F-1D18A9856A87
last_name: Ajanki
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
citation:
ama: Ajanki OH, Erdös L, Krüger TH. Local semicircle law with imprimitive variance
matrix. Electronic Communications in Probability. 2014;19. doi:10.1214/ECP.v19-3121
apa: Ajanki, O. H., Erdös, L., & Krüger, T. H. (2014). Local semicircle law
with imprimitive variance matrix. Electronic Communications in Probability.
Institute of Mathematical Statistics. https://doi.org/10.1214/ECP.v19-3121
chicago: Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Local Semicircle
Law with Imprimitive Variance Matrix.” Electronic Communications in Probability.
Institute of Mathematical Statistics, 2014. https://doi.org/10.1214/ECP.v19-3121.
ieee: O. H. Ajanki, L. Erdös, and T. H. Krüger, “Local semicircle law with imprimitive
variance matrix,” Electronic Communications in Probability, vol. 19. Institute
of Mathematical Statistics, 2014.
ista: Ajanki OH, Erdös L, Krüger TH. 2014. Local semicircle law with imprimitive
variance matrix. Electronic Communications in Probability. 19.
mla: Ajanki, Oskari H., et al. “Local Semicircle Law with Imprimitive Variance Matrix.”
Electronic Communications in Probability, vol. 19, Institute of Mathematical
Statistics, 2014, doi:10.1214/ECP.v19-3121.
short: O.H. Ajanki, L. Erdös, T.H. Krüger, Electronic Communications in Probability
19 (2014).
date_created: 2018-12-11T11:56:10Z
date_published: 2014-06-09T00:00:00Z
date_updated: 2021-01-12T06:55:48Z
day: '09'
ddc:
- '570'
department:
- _id: LaEr
doi: 10.1214/ECP.v19-3121
file:
- access_level: open_access
checksum: bd8a041c76d62fe820bf73ff13ce7d1b
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:09:06Z
date_updated: 2020-07-14T12:45:31Z
file_id: '4729'
file_name: IST-2016-426-v1+1_3121-17518-1-PB.pdf
file_size: 327322
relation: main_file
file_date_updated: 2020-07-14T12:45:31Z
has_accepted_license: '1'
intvolume: ' 19'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
publication: Electronic Communications in Probability
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '4803'
pubrep_id: '426'
quality_controlled: '1'
scopus_import: 1
status: public
title: Local semicircle law with imprimitive variance matrix
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 19
year: '2014'
...