---
_id: '2689'
abstract:
- lang: eng
text: R-type calcium channels (RTCCs) are well known for their role in synaptic
plasticity, but little is known about their subcellular distribution across various
neuronal compartments. Using subtype-specific antibodies, we characterized the
regional and subcellular localization of Ca v2.3 in mice and rats at both light
and electron microscopic levels. Ca v2.3 immunogold particles were found to be
predominantly presynaptic in the interpeduncular nucleus, but postsynaptic in
other brain regions. Serial section analysis of electron microscopic images from
the hippocampal CA1 revealed a higher density of immunogold particles in the dendritic
shaft plasma membrane compared with the pyramidal cell somata. However, the labeling
densities were not significantly different among the apical, oblique, or basal
dendrites. Immunogold particles were also observed over the plasma membrane of
dendritic spines, including both synaptic and extrasynaptic sites. Individual
spine heads contained <20 immunogold particles, with an average density of
~260 immunoparticles per μm 3 spine head volume, in accordance with the density
of RTCCs estimated using calcium imaging (Sabatini and Svoboda, 2000). The Ca
v2.3 density was variable among similar-sized spine heads and did not correlate
with the density in the parent dendrite, implying that spines are individual calcium
compartments operating autonomously from their parent dendrites.
author:
- first_name: Laxmi
full_name: Parajuli, Laxmi K
last_name: Parajuli
- first_name: Chikako
full_name: Nakajima, Chikako
last_name: Nakajima
- first_name: Ákos
full_name: Kulik, Ákos
last_name: Kulik
- first_name: Ko
full_name: Matsui, Ko
last_name: Matsui
- first_name: Toni
full_name: Schneider, Toni
last_name: Schneider
- first_name: Ryuichi
full_name: Ryuichi Shigemoto
id: 499F3ABC-F248-11E8-B48F-1D18A9856A87
last_name: Shigemoto
orcid: 0000-0001-8761-9444
- first_name: Yugo
full_name: Fukazawa, Yugo
last_name: Fukazawa
citation:
ama: Parajuli L, Nakajima C, Kulik Á, et al. Quantitative regional and ultra structural
localization of the Ca v2 3 subunit of R type calcium channel in mouse brain.
Journal of Neuroscience. 2012;32(39):13555-13567. doi:10.1523/JNEUROSCI.1142-12.2012
apa: Parajuli, L., Nakajima, C., Kulik, Á., Matsui, K., Schneider, T., Shigemoto,
R., & Fukazawa, Y. (2012). Quantitative regional and ultra structural localization
of the Ca v2 3 subunit of R type calcium channel in mouse brain. Journal of
Neuroscience. Society for Neuroscience. https://doi.org/10.1523/JNEUROSCI.1142-12.2012
chicago: Parajuli, Laxmi, Chikako Nakajima, Ákos Kulik, Ko Matsui, Toni Schneider,
Ryuichi Shigemoto, and Yugo Fukazawa. “Quantitative Regional and Ultra Structural
Localization of the Ca v2 3 Subunit of R Type Calcium Channel in Mouse Brain.”
Journal of Neuroscience. Society for Neuroscience, 2012. https://doi.org/10.1523/JNEUROSCI.1142-12.2012.
ieee: L. Parajuli et al., “Quantitative regional and ultra structural localization
of the Ca v2 3 subunit of R type calcium channel in mouse brain,” Journal of
Neuroscience, vol. 32, no. 39. Society for Neuroscience, pp. 13555–13567,
2012.
ista: Parajuli L, Nakajima C, Kulik Á, Matsui K, Schneider T, Shigemoto R, Fukazawa
Y. 2012. Quantitative regional and ultra structural localization of the Ca v2
3 subunit of R type calcium channel in mouse brain. Journal of Neuroscience. 32(39),
13555–13567.
mla: Parajuli, Laxmi, et al. “Quantitative Regional and Ultra Structural Localization
of the Ca v2 3 Subunit of R Type Calcium Channel in Mouse Brain.” Journal of
Neuroscience, vol. 32, no. 39, Society for Neuroscience, 2012, pp. 13555–67,
doi:10.1523/JNEUROSCI.1142-12.2012.
short: L. Parajuli, C. Nakajima, Á. Kulik, K. Matsui, T. Schneider, R. Shigemoto,
Y. Fukazawa, Journal of Neuroscience 32 (2012) 13555–13567.
date_created: 2018-12-11T11:59:05Z
date_published: 2012-09-26T00:00:00Z
date_updated: 2021-01-12T06:59:04Z
day: '26'
doi: 10.1523/JNEUROSCI.1142-12.2012
extern: 1
intvolume: ' 32'
issue: '39'
month: '09'
page: 13555 - 13567
publication: Journal of Neuroscience
publication_status: published
publisher: Society for Neuroscience
publist_id: '4208'
quality_controlled: 0
status: public
title: Quantitative regional and ultra structural localization of the Ca v2 3 subunit
of R type calcium channel in mouse brain
type: journal_article
volume: 32
year: '2012'
...
---
_id: '2696'
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
citation:
ama: Erdös L. Universality for random matrices and log-gases. ArXiv. 2012.
apa: Erdös, L. (2012). Universality for random matrices and log-gases. ArXiv.
ArXiv.
chicago: Erdös, László. “Universality for Random Matrices and Log-Gases.” ArXiv.
ArXiv, 2012.
ieee: L. Erdös, “Universality for random matrices and log-gases,” ArXiv.
ArXiv, 2012.
ista: Erdös L. 2012. Universality for random matrices and log-gases. ArXiv, .
mla: Erdös, László. “Universality for Random Matrices and Log-Gases.” ArXiv,
ArXiv, 2012.
short: L. Erdös, ArXiv (2012).
date_created: 2018-12-11T11:59:07Z
date_published: 2012-12-04T00:00:00Z
date_updated: 2021-01-12T06:59:06Z
day: '04'
extern: 1
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1212.0839
month: '12'
oa: 1
publication: ArXiv
publication_status: published
publisher: ArXiv
publist_id: '4201'
quality_controlled: 0
status: public
title: Universality for random matrices and log-gases
type: preprint
year: '2012'
...
---
_id: '2700'
alternative_title:
- Quantum Theory from Small to Large Scales
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
citation:
ama: 'Erdös L. Lecture notes on quantum Brownian motion. In: Vol 95. Oxford University
Press; 2012:3-98.'
apa: Erdös, L. (2012). Lecture notes on quantum Brownian motion (Vol. 95, pp. 3–98).
Presented at the Les Houches Summer School 2010, Oxford University Press.
chicago: Erdös, László. “Lecture Notes on Quantum Brownian Motion,” 95:3–98. Oxford
University Press, 2012.
ieee: L. Erdös, “Lecture notes on quantum Brownian motion,” presented at the Les
Houches Summer School 2010, 2012, vol. 95, pp. 3–98.
ista: Erdös L. 2012. Lecture notes on quantum Brownian motion. Les Houches Summer
School 2010, Quantum Theory from Small to Large Scales, vol. 95, 3–98.
mla: Erdös, László. Lecture Notes on Quantum Brownian Motion. Vol. 95, Oxford
University Press, 2012, pp. 3–98.
short: L. Erdös, in:, Oxford University Press, 2012, pp. 3–98.
conference:
name: Les Houches Summer School 2010
date_created: 2018-12-11T11:59:08Z
date_published: 2012-05-24T00:00:00Z
date_updated: 2021-01-12T06:59:08Z
day: '24'
extern: 1
intvolume: ' 95'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1009.0843
month: '05'
oa: 1
page: 3 - 98
publication_status: published
publisher: Oxford University Press
publist_id: '4196'
quality_controlled: 0
status: public
title: Lecture notes on quantum Brownian motion
type: conference
volume: 95
year: '2012'
...
---
_id: '2715'
abstract:
- lang: eng
text: 'We consider Markov decision processes (MDPs) with specifications given as
Büchi (liveness) objectives. We consider the problem of computing the set of almost-sure
winning vertices from where the objective can be ensured with probability 1. We
study for the first time the average case complexity of the classical algorithm
for computing the set of almost-sure winning vertices for MDPs with Büchi objectives.
Our contributions are as follows: First, we show that for MDPs with constant out-degree
the expected number of iterations is at most logarithmic and the average case
running time is linear (as compared to the worst case linear number of iterations
and quadratic time complexity). Second, for the average case analysis over all
MDPs we show that the expected number of iterations is constant and the average
case running time is linear (again as compared to the worst case linear number
of iterations and quadratic time complexity). Finally we also show that given
that all MDPs are equally likely, the probability that the classical algorithm
requires more than constant number of iterations is exponentially small.'
alternative_title:
- LIPIcs
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Manas
full_name: Joglekar, Manas
last_name: Joglekar
- first_name: Nisarg
full_name: Shah, Nisarg
last_name: Shah
citation:
ama: 'Chatterjee K, Joglekar M, Shah N. Average case analysis of the classical algorithm
for Markov decision processes with Büchi objectives. In: Vol 18. Schloss Dagstuhl
- Leibniz-Zentrum für Informatik; 2012:461-473. doi:10.4230/LIPIcs.FSTTCS.2012.461'
apa: 'Chatterjee, K., Joglekar, M., & Shah, N. (2012). Average case analysis
of the classical algorithm for Markov decision processes with Büchi objectives
(Vol. 18, pp. 461–473). Presented at the FSTTCS: Foundations of Software Technology
and Theoretical Computer Science, Hyderabad, India: Schloss Dagstuhl - Leibniz-Zentrum
für Informatik. https://doi.org/10.4230/LIPIcs.FSTTCS.2012.461'
chicago: Chatterjee, Krishnendu, Manas Joglekar, and Nisarg Shah. “Average Case
Analysis of the Classical Algorithm for Markov Decision Processes with Büchi Objectives,”
18:461–73. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2012. https://doi.org/10.4230/LIPIcs.FSTTCS.2012.461.
ieee: 'K. Chatterjee, M. Joglekar, and N. Shah, “Average case analysis of the classical
algorithm for Markov decision processes with Büchi objectives,” presented at the
FSTTCS: Foundations of Software Technology and Theoretical Computer Science, Hyderabad,
India, 2012, vol. 18, pp. 461–473.'
ista: 'Chatterjee K, Joglekar M, Shah N. 2012. Average case analysis of the classical
algorithm for Markov decision processes with Büchi objectives. FSTTCS: Foundations
of Software Technology and Theoretical Computer Science, LIPIcs, vol. 18, 461–473.'
mla: Chatterjee, Krishnendu, et al. Average Case Analysis of the Classical Algorithm
for Markov Decision Processes with Büchi Objectives. Vol. 18, Schloss Dagstuhl
- Leibniz-Zentrum für Informatik, 2012, pp. 461–73, doi:10.4230/LIPIcs.FSTTCS.2012.461.
short: K. Chatterjee, M. Joglekar, N. Shah, in:, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2012, pp. 461–473.
conference:
end_date: 2012-12-17
location: Hyderabad, India
name: 'FSTTCS: Foundations of Software Technology and Theoretical Computer Science'
start_date: 2012-12-15
date_created: 2018-12-11T11:59:13Z
date_published: 2012-12-10T00:00:00Z
date_updated: 2023-02-23T10:06:04Z
day: '10'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.4230/LIPIcs.FSTTCS.2012.461
ec_funded: 1
file:
- access_level: open_access
checksum: d4d644ed1a885dbfc4fa1ef4c5724dab
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:13:53Z
date_updated: 2020-07-14T12:45:45Z
file_id: '5040'
file_name: IST-2016-525-v1+1_42_1_.pdf
file_size: 519040
relation: main_file
file_date_updated: 2020-07-14T12:45:45Z
has_accepted_license: '1'
intvolume: ' 18'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-nd/4.0/
month: '12'
oa: 1
oa_version: Published Version
page: 461 - 473
project:
- _id: 2584A770-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P 23499-N23
name: Modern Graph Algorithmic Techniques in Formal Verification
- _id: 25863FF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11407
name: Game Theory
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
- _id: 2587B514-B435-11E9-9278-68D0E5697425
name: Microsoft Research Faculty Fellowship
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
publist_id: '4180'
pubrep_id: '525'
quality_controlled: '1'
related_material:
record:
- id: '1598'
relation: later_version
status: public
scopus_import: 1
status: public
title: Average case analysis of the classical algorithm for Markov decision processes
with Büchi objectives
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 18
year: '2012'
...
---
_id: '2767'
abstract:
- lang: eng
text: 'Consider N × N Hermitian or symmetric random matrices H where the distribution
of the (i, j) matrix element is given by a probability measure ν ij with a subexponential
decay. Let σ ij 2 be the variance for the probability measure ν ij with the normalization
property that Σ iσ i,j 2 = 1 for all j. Under essentially the only condition that
c ≤ N σ ij 2 ≤ c -1 for some constant c > 0, we prove that, in the limit N
→ ∞, the eigenvalue spacing statistics of H in the bulk of the spectrum coincide
with those of the Gaussian unitary or orthogonal ensemble (GUE or GOE). We also
show that for band matrices with bandwidth M the local semicircle law holds to
the energy scale M -1. '
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Horng
full_name: Yau, Horng-Tzer
last_name: Yau
- first_name: Jun
full_name: Yin, Jun
last_name: Yin
citation:
ama: Erdös L, Yau H, Yin J. Bulk universality for generalized Wigner matrices. Probability
Theory and Related Fields. 2012;154(1-2):341-407. doi:10.1007/s00440-011-0390-3
apa: Erdös, L., Yau, H., & Yin, J. (2012). Bulk universality for generalized
Wigner matrices. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-011-0390-3
chicago: Erdös, László, Horng Yau, and Jun Yin. “Bulk Universality for Generalized
Wigner Matrices.” Probability Theory and Related Fields. Springer, 2012.
https://doi.org/10.1007/s00440-011-0390-3.
ieee: L. Erdös, H. Yau, and J. Yin, “Bulk universality for generalized Wigner matrices,”
Probability Theory and Related Fields, vol. 154, no. 1–2. Springer, pp.
341–407, 2012.
ista: Erdös L, Yau H, Yin J. 2012. Bulk universality for generalized Wigner matrices.
Probability Theory and Related Fields. 154(1–2), 341–407.
mla: Erdös, László, et al. “Bulk Universality for Generalized Wigner Matrices.”
Probability Theory and Related Fields, vol. 154, no. 1–2, Springer, 2012,
pp. 341–407, doi:10.1007/s00440-011-0390-3.
short: L. Erdös, H. Yau, J. Yin, Probability Theory and Related Fields 154 (2012)
341–407.
date_created: 2018-12-11T11:59:29Z
date_published: 2012-10-01T00:00:00Z
date_updated: 2021-01-12T06:59:33Z
day: '01'
doi: 10.1007/s00440-011-0390-3
extern: 1
intvolume: ' 154'
issue: 1-2
month: '10'
page: 341 - 407
publication: Probability Theory and Related Fields
publication_status: published
publisher: Springer
publist_id: '4123'
quality_controlled: 0
status: public
title: Bulk universality for generalized Wigner matrices
type: journal_article
volume: 154
year: '2012'
...
---
_id: '2768'
abstract:
- lang: eng
text: We consider a two dimensional magnetic Schrödinger operator with a spatially
stationary random magnetic field. We assume that the magnetic field has a positive
lower bound and that it has Fourier modes on arbitrarily short scales. We prove
the Wegner estimate at arbitrary energy, i. e. we show that the averaged density
of states is finite throughout the whole spectrum. We also prove Anderson localization
at the bottom of the spectrum.
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: David
full_name: Hasler, David G
last_name: Hasler
citation:
ama: Erdös L, Hasler D. Wegner estimate and Anderson localization for random magnetic
fields. Communications in Mathematical Physics. 2012;309(2):507-542. doi:10.1007/s00220-011-1373-z
apa: Erdös, L., & Hasler, D. (2012). Wegner estimate and Anderson localization
for random magnetic fields. Communications in Mathematical Physics. Springer.
https://doi.org/10.1007/s00220-011-1373-z
chicago: Erdös, László, and David Hasler. “Wegner Estimate and Anderson Localization
for Random Magnetic Fields.” Communications in Mathematical Physics. Springer,
2012. https://doi.org/10.1007/s00220-011-1373-z.
ieee: L. Erdös and D. Hasler, “Wegner estimate and Anderson localization for random
magnetic fields,” Communications in Mathematical Physics, vol. 309, no.
2. Springer, pp. 507–542, 2012.
ista: Erdös L, Hasler D. 2012. Wegner estimate and Anderson localization for random
magnetic fields. Communications in Mathematical Physics. 309(2), 507–542.
mla: Erdös, László, and David Hasler. “Wegner Estimate and Anderson Localization
for Random Magnetic Fields.” Communications in Mathematical Physics, vol.
309, no. 2, Springer, 2012, pp. 507–42, doi:10.1007/s00220-011-1373-z.
short: L. Erdös, D. Hasler, Communications in Mathematical Physics 309 (2012) 507–542.
date_created: 2018-12-11T11:59:30Z
date_published: 2012-01-01T00:00:00Z
date_updated: 2021-01-12T06:59:34Z
day: '01'
doi: 10.1007/s00220-011-1373-z
extern: 1
intvolume: ' 309'
issue: '2'
month: '01'
page: 507 - 542
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4122'
quality_controlled: 0
status: public
title: Wegner estimate and Anderson localization for random magnetic fields
type: journal_article
volume: 309
year: '2012'
...
---
_id: '2769'
abstract:
- lang: eng
text: We present a generalization of the method of the local relaxation flow to
establish the universality of local spectral statistics of a broad class of large
random matrices. We show that the local distribution of the eigenvalues coincides
with the local statistics of the corresponding Gaussian ensemble provided the
distribution of the individual matrix element is smooth and the eigenvalues {X
J} N j=1 are close to their classical location {y j} N j=1 determined by the limiting
density of eigenvalues. Under the scaling where the typical distance between neighboring
eigenvalues is of order 1/N, the necessary apriori estimate on the location of
eigenvalues requires only to know that E|x j - γ j| 2 ≤ N-1-ε on average. This
information can be obtained by well established methods for various matrix ensembles.
We demonstrate the method by proving local spectral universality for sample covariance
matrices.
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Benjamin
full_name: Schlein, Benjamin
last_name: Schlein
- first_name: Horng
full_name: Yau, Horng-Tzer
last_name: Yau
- first_name: Jun
full_name: Yin, Jun
last_name: Yin
citation:
ama: Erdös L, Schlein B, Yau H, Yin J. The local relaxation flow approach to universality
of the local statistics for random matrices. Annales de l’institut Henri Poincare
(B) Probability and Statistics. 2012;48(1):1-46. doi:10.1214/10-AIHP388
apa: Erdös, L., Schlein, B., Yau, H., & Yin, J. (2012). The local relaxation
flow approach to universality of the local statistics for random matrices. Annales
de l’institut Henri Poincare (B) Probability and Statistics. Institute of
Mathematical Statistics. https://doi.org/10.1214/10-AIHP388
chicago: Erdös, László, Benjamin Schlein, Horng Yau, and Jun Yin. “The Local Relaxation
Flow Approach to Universality of the Local Statistics for Random Matrices.” Annales
de l’institut Henri Poincare (B) Probability and Statistics. Institute of
Mathematical Statistics, 2012. https://doi.org/10.1214/10-AIHP388.
ieee: L. Erdös, B. Schlein, H. Yau, and J. Yin, “The local relaxation flow approach
to universality of the local statistics for random matrices,” Annales de l’institut
Henri Poincare (B) Probability and Statistics, vol. 48, no. 1. Institute of
Mathematical Statistics, pp. 1–46, 2012.
ista: Erdös L, Schlein B, Yau H, Yin J. 2012. The local relaxation flow approach
to universality of the local statistics for random matrices. Annales de l’institut
Henri Poincare (B) Probability and Statistics. 48(1), 1–46.
mla: Erdös, László, et al. “The Local Relaxation Flow Approach to Universality of
the Local Statistics for Random Matrices.” Annales de l’institut Henri Poincare
(B) Probability and Statistics, vol. 48, no. 1, Institute of Mathematical
Statistics, 2012, pp. 1–46, doi:10.1214/10-AIHP388.
short: L. Erdös, B. Schlein, H. Yau, J. Yin, Annales de l’institut Henri Poincare
(B) Probability and Statistics 48 (2012) 1–46.
date_created: 2018-12-11T11:59:30Z
date_published: 2012-02-01T00:00:00Z
date_updated: 2021-01-12T06:59:34Z
day: '01'
doi: 10.1214/10-AIHP388
extern: 1
intvolume: ' 48'
issue: '1'
month: '02'
page: 1 - 46
publication: Annales de l'institut Henri Poincare (B) Probability and Statistics
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '4121'
quality_controlled: 0
status: public
title: The local relaxation flow approach to universality of the local statistics
for random matrices
type: journal_article
volume: 48
year: '2012'
...
---
_id: '2770'
abstract:
- lang: eng
text: 'Consider N×N Hermitian or symmetric random matrices H with independent entries,
where the distribution of the (i,j) matrix element is given by the probability
measure vij with zero expectation and with variance σ ιj 2. We assume that the
variances satisfy the normalization condition Σiσij2=1 for all j and that there
is a positive constant c such that c≤Nσ ιj 2 ιc -1. We further assume that the
probability distributions νij have a uniform subexponential decay. We prove that
the Stieltjes transform of the empirical eigenvalue distribution of H is given
by the Wigner semicircle law uniformly up to the edges of the spectrum with an
error of order (Nη) -1 where η is the imaginary part of the spectral parameter
in the Stieltjes transform. There are three corollaries to this strong local semicircle
law: (1) Rigidity of eigenvalues: If γj=γj,N denotes the classical location of
the j-th eigenvalue under the semicircle law ordered in increasing order, then
the j-th eigenvalue λj is close to γj in the sense that for some positive constants
C, c P{double-struck}(∃j:|λ j-γ j|≥(logN) CloglogN[min(j,N-j+1)] -1/3N -2/3)≤
C exp[-(logN) cloglogN] for N large enough. (2) The proof of Dyson''s conjecture
(Dyson, 1962 [15]) which states that the time scale of the Dyson Brownian motion
to reach local equilibrium is of order N -1 up to logarithmic corrections. (3)
The edge universality holds in the sense that the probability distributions of
the largest (and the smallest) eigenvalues of two generalized Wigner ensembles
are the same in the large N limit provided that the second moments of the two
ensembles are identical.'
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Horng
full_name: Yau, Horng-Tzer
last_name: Yau
- first_name: Jun
full_name: Yin, Jun
last_name: Yin
citation:
ama: Erdös L, Yau H, Yin J. Rigidity of eigenvalues of generalized Wigner matrices.
Advances in Mathematics. 2012;229(3):1435-1515. doi:10.1016/j.aim.2011.12.010
apa: Erdös, L., Yau, H., & Yin, J. (2012). Rigidity of eigenvalues of generalized
Wigner matrices. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2011.12.010
chicago: Erdös, László, Horng Yau, and Jun Yin. “Rigidity of Eigenvalues of Generalized
Wigner Matrices.” Advances in Mathematics. Academic Press, 2012. https://doi.org/10.1016/j.aim.2011.12.010.
ieee: L. Erdös, H. Yau, and J. Yin, “Rigidity of eigenvalues of generalized Wigner
matrices,” Advances in Mathematics, vol. 229, no. 3. Academic Press, pp.
1435–1515, 2012.
ista: Erdös L, Yau H, Yin J. 2012. Rigidity of eigenvalues of generalized Wigner
matrices. Advances in Mathematics. 229(3), 1435–1515.
mla: Erdös, László, et al. “Rigidity of Eigenvalues of Generalized Wigner Matrices.”
Advances in Mathematics, vol. 229, no. 3, Academic Press, 2012, pp. 1435–515,
doi:10.1016/j.aim.2011.12.010.
short: L. Erdös, H. Yau, J. Yin, Advances in Mathematics 229 (2012) 1435–1515.
date_created: 2018-12-11T11:59:30Z
date_published: 2012-02-15T00:00:00Z
date_updated: 2021-01-12T06:59:35Z
day: '15'
doi: 10.1016/j.aim.2011.12.010
extern: 1
intvolume: ' 229'
issue: '3'
month: '02'
page: 1435 - 1515
publication: Advances in Mathematics
publication_status: published
publisher: Academic Press
publist_id: '4120'
quality_controlled: 0
status: public
title: Rigidity of eigenvalues of generalized Wigner matrices
type: journal_article
volume: 229
year: '2012'
...
---
_id: '2771'
abstract:
- lang: eng
text: We consider a magnetic Schrödinger operator in two dimensions. The magnetic
field is given as the sum of a large and constant magnetic field and a random
magnetic field. Moreover, we allow for an additional deterministic potential as
well as a magnetic field which are both periodic. We show that the spectrum of
this operator is contained in broadened bands around the Landau levels and that
the edges of these bands consist of pure point spectrum with exponentially decaying
eigenfunctions. The proof is based on a recent Wegner estimate obtained in Erdos
and Hasler (Commun. Math. Phys., preprint, arXiv:1012.5185) and a multiscale analysis.
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: David
full_name: Hasler, David G
last_name: Hasler
citation:
ama: Erdös L, Hasler D. Anderson localization at band edges for random magnetic
fields. Journal of Statistical Physics. 2012;146(5):900-923. doi:10.1007/s10955-012-0445-6
apa: Erdös, L., & Hasler, D. (2012). Anderson localization at band edges for
random magnetic fields. Journal of Statistical Physics. Springer. https://doi.org/10.1007/s10955-012-0445-6
chicago: Erdös, László, and David Hasler. “Anderson Localization at Band Edges for
Random Magnetic Fields.” Journal of Statistical Physics. Springer, 2012.
https://doi.org/10.1007/s10955-012-0445-6.
ieee: L. Erdös and D. Hasler, “Anderson localization at band edges for random magnetic
fields,” Journal of Statistical Physics, vol. 146, no. 5. Springer, pp.
900–923, 2012.
ista: Erdös L, Hasler D. 2012. Anderson localization at band edges for random magnetic
fields. Journal of Statistical Physics. 146(5), 900–923.
mla: Erdös, László, and David Hasler. “Anderson Localization at Band Edges for Random
Magnetic Fields.” Journal of Statistical Physics, vol. 146, no. 5, Springer,
2012, pp. 900–23, doi:10.1007/s10955-012-0445-6.
short: L. Erdös, D. Hasler, Journal of Statistical Physics 146 (2012) 900–923.
date_created: 2018-12-11T11:59:31Z
date_published: 2012-03-01T00:00:00Z
date_updated: 2021-01-12T06:59:35Z
day: '01'
doi: 10.1007/s10955-012-0445-6
extern: 1
intvolume: ' 146'
issue: '5'
month: '03'
page: 900 - 923
publication: Journal of Statistical Physics
publication_status: published
publisher: Springer
publist_id: '4119'
quality_controlled: 0
status: public
title: Anderson localization at band edges for random magnetic fields
type: journal_article
volume: 146
year: '2012'
...
---
_id: '2772'
abstract:
- lang: eng
text: We consider the semiclassical asymptotics of the sum of negative eigenvalues
of the three-dimensional Pauli operator with an external potential and a self-generated
magnetic field B. We also add the field energy β ∫ B 2 and we minimize over all
magnetic fields. The parameter β effectively determines the strength of the field.
We consider the weak field regime with βh 2 ≥ const > 0, where h is the semiclassical
parameter. For smooth potentials we prove that the semiclassical asymptotics of
the total energy is given by the non-magnetic Weyl term to leading order with
an error bound that is smaller by a factor h 1+e{open}, i. e. the subleading term
vanishes. However for potentials with a Coulomb singularity, the subleading term
does not vanish due to the non-semiclassical effect of the singularity. Combined
with a multiscale technique, this refined estimate is used in the companion paper
(Erdo{double acute}s et al. in Scott correction for large molecules with a self-generated
magnetic field, Preprint, 2011) to prove the second order Scott correction to
the ground state energy of large atoms and molecules.
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Søren
full_name: Fournais, Søren
last_name: Fournais
- first_name: Jan
full_name: Solovej, Jan P
last_name: Solovej
citation:
ama: Erdös L, Fournais S, Solovej J. Second order semiclassics with self generated
magnetic fields. Annales Henri Poincare. 2012;13(4):671-730. doi:10.1007/s00023-011-0150-z
apa: Erdös, L., Fournais, S., & Solovej, J. (2012). Second order semiclassics
with self generated magnetic fields. Annales Henri Poincare. Birkhäuser.
https://doi.org/10.1007/s00023-011-0150-z
chicago: Erdös, László, Søren Fournais, and Jan Solovej. “Second Order Semiclassics
with Self Generated Magnetic Fields.” Annales Henri Poincare. Birkhäuser,
2012. https://doi.org/10.1007/s00023-011-0150-z.
ieee: L. Erdös, S. Fournais, and J. Solovej, “Second order semiclassics with self
generated magnetic fields,” Annales Henri Poincare, vol. 13, no. 4. Birkhäuser,
pp. 671–730, 2012.
ista: Erdös L, Fournais S, Solovej J. 2012. Second order semiclassics with self
generated magnetic fields. Annales Henri Poincare. 13(4), 671–730.
mla: Erdös, László, et al. “Second Order Semiclassics with Self Generated Magnetic
Fields.” Annales Henri Poincare, vol. 13, no. 4, Birkhäuser, 2012, pp.
671–730, doi:10.1007/s00023-011-0150-z.
short: L. Erdös, S. Fournais, J. Solovej, Annales Henri Poincare 13 (2012) 671–730.
date_created: 2018-12-11T11:59:31Z
date_published: 2012-05-01T00:00:00Z
date_updated: 2021-01-12T06:59:36Z
day: '01'
doi: 10.1007/s00023-011-0150-z
extern: 1
intvolume: ' 13'
issue: '4'
month: '05'
page: 671 - 730
publication: Annales Henri Poincare
publication_status: published
publisher: Birkhäuser
publist_id: '4118'
quality_controlled: 0
status: public
title: Second order semiclassics with self generated magnetic fields
type: journal_article
volume: 13
year: '2012'
...
---
_id: '2773'
abstract:
- lang: eng
text: Recently we proved [3, 4, 6, 7, 9, 10, 11] that the eigenvalue correlation
functions of a general class of random matrices converge, weakly with respect
to the energy, to the corresponding ones of Gaussian matrices. Tao and Vu [15]
gave a proof that for the special case of Hermitian Wigner matrices the convergence
can be strengthened to vague convergence at any fixed energy in the bulk. In this
article we show that this theorem is an immediate corollary of our earlier results.
Indeed, a more general form of this theorem also follows directly from our work
[2].
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Horng
full_name: Yau, Horng-Tzer
last_name: Yau
citation:
ama: Erdös L, Yau H. A comment on the Wigner-Dyson-Mehta bulk universality conjecture
for Wigner matrices. Electronic Journal of Probability. 2012;17. doi:10.1214/EJP.v17-1779
apa: Erdös, L., & Yau, H. (2012). A comment on the Wigner-Dyson-Mehta bulk universality
conjecture for Wigner matrices. Electronic Journal of Probability. Institute
of Mathematical Statistics. https://doi.org/10.1214/EJP.v17-1779
chicago: Erdös, László, and Horng Yau. “A Comment on the Wigner-Dyson-Mehta Bulk
Universality Conjecture for Wigner Matrices.” Electronic Journal of Probability.
Institute of Mathematical Statistics, 2012. https://doi.org/10.1214/EJP.v17-1779.
ieee: L. Erdös and H. Yau, “A comment on the Wigner-Dyson-Mehta bulk universality
conjecture for Wigner matrices,” Electronic Journal of Probability, vol.
17. Institute of Mathematical Statistics, 2012.
ista: Erdös L, Yau H. 2012. A comment on the Wigner-Dyson-Mehta bulk universality
conjecture for Wigner matrices. Electronic Journal of Probability. 17.
mla: Erdös, László, and Horng Yau. “A Comment on the Wigner-Dyson-Mehta Bulk Universality
Conjecture for Wigner Matrices.” Electronic Journal of Probability, vol.
17, Institute of Mathematical Statistics, 2012, doi:10.1214/EJP.v17-1779.
short: L. Erdös, H. Yau, Electronic Journal of Probability 17 (2012).
date_created: 2018-12-11T11:59:31Z
date_published: 2012-04-10T00:00:00Z
date_updated: 2021-01-12T06:59:36Z
day: '10'
doi: 10.1214/EJP.v17-1779
extern: 1
intvolume: ' 17'
month: '04'
publication: Electronic Journal of Probability
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '4117'
quality_controlled: 0
status: public
title: A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner
matrices
type: journal_article
volume: 17
year: '2012'
...
---
_id: '2774'
abstract:
- lang: eng
text: We consider a large neutral molecule with total nuclear charge Z in non-relativistic
quantum mechanics with a self-generated classical electromagnetic field. To ensure
stability, we assume that Zα 2 ≤ κ 0 for a sufficiently small κ 0, where α denotes
the fine structure constant. We show that, in the simultaneous limit Z → ∞, α
→ 0 such that κ = Zα 2 is fixed, the ground state energy of the system is given
by a two term expansion c 1Z 7/3 + c 2(κ) Z 2 + o(Z 2). The leading term is given
by the non-magnetic Thomas-Fermi theory. Our result shows that the magnetic field
affects only the second (so-called Scott) term in the expansion.
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Søren
full_name: Fournais, Søren
last_name: Fournais
- first_name: Jan
full_name: Solovej, Jan P
last_name: Solovej
citation:
ama: Erdös L, Fournais S, Solovej J. Scott correction for large atoms and molecules
in a self-generated magnetic field. Communications in Mathematical Physics.
2012;312(3):847-882. doi:10.1007/s00220-012-1468-1
apa: Erdös, L., Fournais, S., & Solovej, J. (2012). Scott correction for large
atoms and molecules in a self-generated magnetic field. Communications in Mathematical
Physics. Springer. https://doi.org/10.1007/s00220-012-1468-1
chicago: Erdös, László, Søren Fournais, and Jan Solovej. “Scott Correction for Large
Atoms and Molecules in a Self-Generated Magnetic Field.” Communications in
Mathematical Physics. Springer, 2012. https://doi.org/10.1007/s00220-012-1468-1.
ieee: L. Erdös, S. Fournais, and J. Solovej, “Scott correction for large atoms and
molecules in a self-generated magnetic field,” Communications in Mathematical
Physics, vol. 312, no. 3. Springer, pp. 847–882, 2012.
ista: Erdös L, Fournais S, Solovej J. 2012. Scott correction for large atoms and
molecules in a self-generated magnetic field. Communications in Mathematical Physics.
312(3), 847–882.
mla: Erdös, László, et al. “Scott Correction for Large Atoms and Molecules in a
Self-Generated Magnetic Field.” Communications in Mathematical Physics,
vol. 312, no. 3, Springer, 2012, pp. 847–82, doi:10.1007/s00220-012-1468-1.
short: L. Erdös, S. Fournais, J. Solovej, Communications in Mathematical Physics
312 (2012) 847–882.
date_created: 2018-12-11T11:59:31Z
date_published: 2012-06-01T00:00:00Z
date_updated: 2021-01-12T06:59:36Z
day: '01'
doi: 10.1007/s00220-012-1468-1
extern: 1
intvolume: ' 312'
issue: '3'
month: '06'
page: 847 - 882
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4116'
quality_controlled: 0
status: public
title: Scott correction for large atoms and molecules in a self-generated magnetic
field
type: journal_article
volume: 312
year: '2012'
...
---
_id: '2775'
abstract:
- lang: eng
text: The Wigner-Dyson-Gaudin-Mehta conjecture asserts that the local eigenvalue
statistics of large random matrices exhibit universal behavior depending only
on the symmetry class of the matrix ensemble. For invariant matrix models, the
eigenvalue distributions are given by a log-gas with potential V and inverse temperature
β = 1, 2, 4, corresponding to the orthogonal, unitary and symplectic ensembles.
For β ∉ {1, 2, 4}, there is no natural random matrix ensemble behind this model,
but the statistical physics interpretation of the log-gas is still valid for all
β > 0. The universality conjecture for invariant ensembles asserts that the
local eigenvalue statistics are independent of V. In this article, we review our
recent solution to the universality conjecture for both invariant and non-invariant
ensembles. We will also demonstrate that the local ergodicity of the Dyson Brownian
motion is the intrinsic mechanism behind the universality. Furthermore, we review
the solution of Dyson's conjecture on the local relaxation time of the Dyson Brownian
motion. Related questions such as delocalization of eigenvectors and local version
of Wigner's semicircle law will also be discussed.
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Horng
full_name: Yau, Horng-Tzer
last_name: Yau
citation:
ama: Erdös L, Yau H. Universality of local spectral statistics of random matrices.
Bulletin of the American Mathematical Society. 2012;49(3):377-414. doi:10.1090/S0273-0979-2012-01372-1
apa: Erdös, L., & Yau, H. (2012). Universality of local spectral statistics
of random matrices. Bulletin of the American Mathematical Society. American
Mathematical Society. https://doi.org/10.1090/S0273-0979-2012-01372-1
chicago: Erdös, László, and Horng Yau. “Universality of Local Spectral Statistics
of Random Matrices.” Bulletin of the American Mathematical Society. American
Mathematical Society, 2012. https://doi.org/10.1090/S0273-0979-2012-01372-1.
ieee: L. Erdös and H. Yau, “Universality of local spectral statistics of random
matrices,” Bulletin of the American Mathematical Society, vol. 49, no.
3. American Mathematical Society, pp. 377–414, 2012.
ista: Erdös L, Yau H. 2012. Universality of local spectral statistics of random
matrices. Bulletin of the American Mathematical Society. 49(3), 377–414.
mla: Erdös, László, and Horng Yau. “Universality of Local Spectral Statistics of
Random Matrices.” Bulletin of the American Mathematical Society, vol. 49,
no. 3, American Mathematical Society, 2012, pp. 377–414, doi:10.1090/S0273-0979-2012-01372-1.
short: L. Erdös, H. Yau, Bulletin of the American Mathematical Society 49 (2012)
377–414.
date_created: 2018-12-11T11:59:32Z
date_published: 2012-01-30T00:00:00Z
date_updated: 2021-01-12T06:59:36Z
day: '30'
doi: 10.1090/S0273-0979-2012-01372-1
extern: 1
intvolume: ' 49'
issue: '3'
month: '01'
page: 377 - 414
publication: Bulletin of the American Mathematical Society
publication_status: published
publisher: American Mathematical Society
publist_id: '4115'
quality_controlled: 0
status: public
title: Universality of local spectral statistics of random matrices
type: journal_article
volume: 49
year: '2012'
...
---
_id: '2776'
abstract:
- lang: eng
text: We consider the ensemble of adjacency matrices of Erdős-Rényi random graphs,
i.e. graphs on N vertices where every edge is chosen independently and with probability
p ≡ p(N). We rescale the matrix so that its bulk eigenvalues are of order one.
Under the assumption pN≫N2/3 , we prove the universality of eigenvalue distributions
both in the bulk and at the edge of the spectrum. More precisely, we prove (1)
that the eigenvalue spacing of the Erdős-Rényi graph in the bulk of the spectrum
has the same distribution as that of the Gaussian orthogonal ensemble; and (2)
that the second largest eigenvalue of the Erdős-Rényi graph has the same distribution
as the largest eigenvalue of the Gaussian orthogonal ensemble. As an application
of our method, we prove the bulk universality of generalized Wigner matrices under
the assumption that the matrix entries have at least 4 + ε moments.
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Antti
full_name: Knowles, Antti
last_name: Knowles
- first_name: Horng
full_name: Yau, Horng-Tzer
last_name: Yau
- first_name: Jun
full_name: Yin, Jun
last_name: Yin
citation:
ama: 'Erdös L, Knowles A, Yau H, Yin J. Spectral statistics of Erdős-Rényi graphs
II: Eigenvalue spacing and the extreme eigenvalues. Communications in Mathematical
Physics. 2012;314(3):587-640. doi:10.1007/s00220-012-1527-7'
apa: 'Erdös, L., Knowles, A., Yau, H., & Yin, J. (2012). Spectral statistics
of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues. Communications
in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-012-1527-7'
chicago: 'Erdös, László, Antti Knowles, Horng Yau, and Jun Yin. “Spectral Statistics
of Erdős-Rényi Graphs II: Eigenvalue Spacing and the Extreme Eigenvalues.” Communications
in Mathematical Physics. Springer, 2012. https://doi.org/10.1007/s00220-012-1527-7.'
ieee: 'L. Erdös, A. Knowles, H. Yau, and J. Yin, “Spectral statistics of Erdős-Rényi
graphs II: Eigenvalue spacing and the extreme eigenvalues,” Communications
in Mathematical Physics, vol. 314, no. 3. Springer, pp. 587–640, 2012.'
ista: 'Erdös L, Knowles A, Yau H, Yin J. 2012. Spectral statistics of Erdős-Rényi
graphs II: Eigenvalue spacing and the extreme eigenvalues. Communications in Mathematical
Physics. 314(3), 587–640.'
mla: 'Erdös, László, et al. “Spectral Statistics of Erdős-Rényi Graphs II: Eigenvalue
Spacing and the Extreme Eigenvalues.” Communications in Mathematical Physics,
vol. 314, no. 3, Springer, 2012, pp. 587–640, doi:10.1007/s00220-012-1527-7.'
short: L. Erdös, A. Knowles, H. Yau, J. Yin, Communications in Mathematical Physics
314 (2012) 587–640.
date_created: 2018-12-11T11:59:32Z
date_published: 2012-09-01T00:00:00Z
date_updated: 2021-01-12T06:59:37Z
day: '01'
doi: 10.1007/s00220-012-1527-7
extern: 1
intvolume: ' 314'
issue: '3'
month: '09'
page: 587 - 640
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4114'
quality_controlled: 0
status: public
title: 'Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme
eigenvalues'
type: journal_article
volume: 314
year: '2012'
...
---
_id: '2777'
abstract:
- lang: eng
text: We consider a large neutral molecule with total nuclear charge Z in a model
with self-generated classical magnetic field and where the kinetic energy of the
electrons is treated relativistically. To ensure stability, we assume that Zα
< 2/π, where α denotes the fine structure constant. We are interested in the
ground state energy in the simultaneous limit Z → ∞, α → 0 such that κ = Zα is
fixed. The leading term in the energy asymptotics is independent of κ, it is given
by the Thomas-Fermi energy of order Z7/3 and it is unchanged by including the
self-generated magnetic field. We prove the first correction term to this energy,
the so-called Scott correction of the form S(αZ)Z2. The current paper extends
the result of Solovej et al. [Commun. Pure Appl. Math.LXIII, 39-118 (2010)] on
the Scott correction for relativistic molecules to include a self-generated magnetic
field. Furthermore, we show that the corresponding Scott correction function S,
first identified by Solovej et al. [Commun. Pure Appl. Math.LXIII, 39-118 (2010)],
is unchanged by including a magnetic field. We also prove new Lieb-Thirring inequalities
for the relativistic kinetic energy with magnetic fields.
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Søren
full_name: Fournais, Søren
last_name: Fournais
- first_name: Jan
full_name: Solovej, Jan P
last_name: Solovej
citation:
ama: Erdös L, Fournais S, Solovej J. Relativistic Scott correction in self-generated
magnetic fields. Journal of Mathematical Physics. 2012;53(9). doi:10.1063/1.3697417
apa: Erdös, L., Fournais, S., & Solovej, J. (2012). Relativistic Scott correction
in self-generated magnetic fields. Journal of Mathematical Physics. American
Institute of Physics. https://doi.org/10.1063/1.3697417
chicago: Erdös, László, Søren Fournais, and Jan Solovej. “Relativistic Scott Correction
in Self-Generated Magnetic Fields.” Journal of Mathematical Physics. American
Institute of Physics, 2012. https://doi.org/10.1063/1.3697417.
ieee: L. Erdös, S. Fournais, and J. Solovej, “Relativistic Scott correction in self-generated
magnetic fields,” Journal of Mathematical Physics, vol. 53, no. 9. American
Institute of Physics, 2012.
ista: Erdös L, Fournais S, Solovej J. 2012. Relativistic Scott correction in self-generated
magnetic fields. Journal of Mathematical Physics. 53(9).
mla: Erdös, László, et al. “Relativistic Scott Correction in Self-Generated Magnetic
Fields.” Journal of Mathematical Physics, vol. 53, no. 9, American Institute
of Physics, 2012, doi:10.1063/1.3697417.
short: L. Erdös, S. Fournais, J. Solovej, Journal of Mathematical Physics 53 (2012).
date_created: 2018-12-11T11:59:32Z
date_published: 2012-09-28T00:00:00Z
date_updated: 2021-01-12T06:59:37Z
day: '28'
doi: 10.1063/1.3697417
extern: 1
intvolume: ' 53'
issue: '9'
month: '09'
publication: Journal of Mathematical Physics
publication_status: published
publisher: American Institute of Physics
publist_id: '4113'
quality_controlled: 0
status: public
title: Relativistic Scott correction in self-generated magnetic fields
type: journal_article
volume: 53
year: '2012'
...
---
_id: '2778'
abstract:
- lang: eng
text: We prove the bulk universality of the β-ensembles with non-convex regular
analytic potentials for any β > 0. This removes the convexity assumption appeared
in the earlier work [P. Bourgade, L. Erdös, and H.-T. Yau, Universality of general
β-ensembles, preprint arXiv:0907.5605 (2011)]. The convexity condition enabled
us to use the logarithmic Sobolev inequality to estimate events with small probability.
The new idea is to introduce a "convexified measure" so that the local
statistics are preserved under this convexification.
author:
- first_name: Paul
full_name: Bourgade, Paul
last_name: Bourgade
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Horng
full_name: Yau, Horng-Tzer
last_name: Yau
citation:
ama: Bourgade P, Erdös L, Yau H. Bulk universality of general β-ensembles with non-convex
potential. Journal of Mathematical Physics. 2012;53(9). doi:10.1063/1.4751478
apa: Bourgade, P., Erdös, L., & Yau, H. (2012). Bulk universality of general
β-ensembles with non-convex potential. Journal of Mathematical Physics.
American Institute of Physics. https://doi.org/10.1063/1.4751478
chicago: Bourgade, Paul, László Erdös, and Horng Yau. “Bulk Universality of General
β-Ensembles with Non-Convex Potential.” Journal of Mathematical Physics.
American Institute of Physics, 2012. https://doi.org/10.1063/1.4751478.
ieee: P. Bourgade, L. Erdös, and H. Yau, “Bulk universality of general β-ensembles
with non-convex potential,” Journal of Mathematical Physics, vol. 53, no.
9. American Institute of Physics, 2012.
ista: Bourgade P, Erdös L, Yau H. 2012. Bulk universality of general β-ensembles
with non-convex potential. Journal of Mathematical Physics. 53(9).
mla: Bourgade, Paul, et al. “Bulk Universality of General β-Ensembles with Non-Convex
Potential.” Journal of Mathematical Physics, vol. 53, no. 9, American Institute
of Physics, 2012, doi:10.1063/1.4751478.
short: P. Bourgade, L. Erdös, H. Yau, Journal of Mathematical Physics 53 (2012).
date_created: 2018-12-11T11:59:33Z
date_published: 2012-09-28T00:00:00Z
date_updated: 2021-01-12T06:59:38Z
day: '28'
doi: 10.1063/1.4751478
extern: 1
intvolume: ' 53'
issue: '9'
month: '09'
publication: Journal of Mathematical Physics
publication_status: published
publisher: American Institute of Physics
publist_id: '4112'
quality_controlled: 0
status: public
title: Bulk universality of general β-ensembles with non-convex potential
type: journal_article
volume: 53
year: '2012'
...
---
_id: '2779'
abstract:
- lang: eng
text: We consider a two-dimensional magnetic Schrödinger operator on a square lattice
with a spatially stationary random magnetic field. We prove Anderson localization
near the spectral edges. We use a new approach to establish a Wegner estimate
that does not rely on the monotonicity of the energy on the random parameters.
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: David
full_name: Hasler, David G
last_name: Hasler
citation:
ama: Erdös L, Hasler D. Wegner estimate for random magnetic Laplacian on ℤ 2. Annales
Henri Poincare. 2012;13(8):1719-1731. doi:10.1007/s00023-012-0177-9
apa: Erdös, L., & Hasler, D. (2012). Wegner estimate for random magnetic Laplacian
on ℤ 2. Annales Henri Poincare. Birkhäuser. https://doi.org/10.1007/s00023-012-0177-9
chicago: Erdös, László, and David Hasler. “Wegner Estimate for Random Magnetic Laplacian
on ℤ 2.” Annales Henri Poincare. Birkhäuser, 2012. https://doi.org/10.1007/s00023-012-0177-9.
ieee: L. Erdös and D. Hasler, “Wegner estimate for random magnetic Laplacian on
ℤ 2,” Annales Henri Poincare, vol. 13, no. 8. Birkhäuser, pp. 1719–1731,
2012.
ista: Erdös L, Hasler D. 2012. Wegner estimate for random magnetic Laplacian on
ℤ 2. Annales Henri Poincare. 13(8), 1719–1731.
mla: Erdös, László, and David Hasler. “Wegner Estimate for Random Magnetic Laplacian
on ℤ 2.” Annales Henri Poincare, vol. 13, no. 8, Birkhäuser, 2012, pp.
1719–31, doi:10.1007/s00023-012-0177-9.
short: L. Erdös, D. Hasler, Annales Henri Poincare 13 (2012) 1719–1731.
date_created: 2018-12-11T11:59:33Z
date_published: 2012-12-01T00:00:00Z
date_updated: 2021-01-12T06:59:38Z
day: '01'
doi: 10.1007/s00023-012-0177-9
extern: 1
intvolume: ' 13'
issue: '8'
month: '12'
page: 1719 - 1731
publication: Annales Henri Poincare
publication_status: published
publisher: Birkhäuser
publist_id: '4111'
quality_controlled: 0
status: public
title: Wegner estimate for random magnetic Laplacian on ℤ 2
type: journal_article
volume: 13
year: '2012'
...
---
_id: '2802'
abstract:
- lang: eng
text: When a binary fluid demixes under a slow temperature ramp, nucleation, coarsening
and sedimentation of droplets lead to an oscillatory evolution of the phase-separating
system. The advection of the sedimenting droplets is found to be chaotic. The
flow is driven by density differences between two phases. Here, we show how image
processing can be combined with particle tracking to resolve droplet size and
velocity simultaneously. Droplets are used as tracer particles, and the sedimentation
velocity is determined. Taking these effects into account, droplets with radii
in the range of 4-40 μm are detected and tracked. Based on these data, we resolve
the oscillations in the droplet size distribution that are coupled to the convective
flow.
author:
- first_name: Tobias
full_name: Lapp, Tobias
last_name: Lapp
- first_name: Martin
full_name: Rohloff, Martin
last_name: Rohloff
- first_name: Jürgen
full_name: Vollmer, Jürgen T
last_name: Vollmer
- first_name: Björn
full_name: Björn Hof
id: 3A374330-F248-11E8-B48F-1D18A9856A87
last_name: Hof
orcid: 0000-0003-2057-2754
citation:
ama: Lapp T, Rohloff M, Vollmer J, Hof B. Particle tracking for polydisperse sedimenting
droplets in phase separation. Experiments in Fluids. 2012;52(5):1187-1200.
doi:10.1007/s00348-011-1243-7
apa: Lapp, T., Rohloff, M., Vollmer, J., & Hof, B. (2012). Particle tracking
for polydisperse sedimenting droplets in phase separation. Experiments in Fluids.
Springer. https://doi.org/10.1007/s00348-011-1243-7
chicago: Lapp, Tobias, Martin Rohloff, Jürgen Vollmer, and Björn Hof. “Particle
Tracking for Polydisperse Sedimenting Droplets in Phase Separation.” Experiments
in Fluids. Springer, 2012. https://doi.org/10.1007/s00348-011-1243-7.
ieee: T. Lapp, M. Rohloff, J. Vollmer, and B. Hof, “Particle tracking for polydisperse
sedimenting droplets in phase separation,” Experiments in Fluids, vol.
52, no. 5. Springer, pp. 1187–1200, 2012.
ista: Lapp T, Rohloff M, Vollmer J, Hof B. 2012. Particle tracking for polydisperse
sedimenting droplets in phase separation. Experiments in Fluids. 52(5), 1187–1200.
mla: Lapp, Tobias, et al. “Particle Tracking for Polydisperse Sedimenting Droplets
in Phase Separation.” Experiments in Fluids, vol. 52, no. 5, Springer,
2012, pp. 1187–200, doi:10.1007/s00348-011-1243-7.
short: T. Lapp, M. Rohloff, J. Vollmer, B. Hof, Experiments in Fluids 52 (2012)
1187–1200.
date_created: 2018-12-11T11:59:40Z
date_published: 2012-05-05T00:00:00Z
date_updated: 2021-01-12T06:59:49Z
day: '05'
doi: 10.1007/s00348-011-1243-7
extern: 1
intvolume: ' 52'
issue: '5'
month: '05'
page: 1187 - 1200
publication: Experiments in Fluids
publication_status: published
publisher: Springer
publist_id: '4087'
quality_controlled: 0
status: public
title: Particle tracking for polydisperse sedimenting droplets in phase separation
type: journal_article
volume: 52
year: '2012'
...
---
_id: '2803'
abstract:
- lang: eng
text: Recent numerical studies suggest that in pipe and related shear flows, the
region of phase space separating laminar from turbulent motion is organized by
a chaotic attractor, called an edge state, which mediates the transition process.
We here confirm the existence of the edge state in laboratory experiments. We
observe that it governs the dynamics during the decay of turbulence underlining
its potential relevance for turbulence control. In addition we unveil two unstable
traveling wave solutions underlying the experimental flow fields. This observation
corroborates earlier suggestions that unstable solutions organize turbulence and
its stability border.
author:
- first_name: Alberto
full_name: de Lózar, Alberto
last_name: De Lózar
- first_name: Fernando
full_name: Mellibovsky, Fernando
last_name: Mellibovsky
- first_name: Marc
full_name: Avila, Marc
last_name: Avila
- first_name: Björn
full_name: Björn Hof
id: 3A374330-F248-11E8-B48F-1D18A9856A87
last_name: Hof
orcid: 0000-0003-2057-2754
citation:
ama: De Lózar A, Mellibovsky F, Avila M, Hof B. Edge state in pipe flow experiments.
Physical Review Letters. 2012;108(21). doi:10.1103/PhysRevLett.108.214502
apa: De Lózar, A., Mellibovsky, F., Avila, M., & Hof, B. (2012). Edge state
in pipe flow experiments. Physical Review Letters. American Physical Society.
https://doi.org/10.1103/PhysRevLett.108.214502
chicago: De Lózar, Alberto, Fernando Mellibovsky, Marc Avila, and Björn Hof. “Edge
State in Pipe Flow Experiments.” Physical Review Letters. American Physical
Society, 2012. https://doi.org/10.1103/PhysRevLett.108.214502.
ieee: A. De Lózar, F. Mellibovsky, M. Avila, and B. Hof, “Edge state in pipe flow
experiments,” Physical Review Letters, vol. 108, no. 21. American Physical
Society, 2012.
ista: De Lózar A, Mellibovsky F, Avila M, Hof B. 2012. Edge state in pipe flow experiments.
Physical Review Letters. 108(21).
mla: De Lózar, Alberto, et al. “Edge State in Pipe Flow Experiments.” Physical
Review Letters, vol. 108, no. 21, American Physical Society, 2012, doi:10.1103/PhysRevLett.108.214502.
short: A. De Lózar, F. Mellibovsky, M. Avila, B. Hof, Physical Review Letters 108
(2012).
date_created: 2018-12-11T11:59:41Z
date_published: 2012-05-21T00:00:00Z
date_updated: 2021-01-12T06:59:49Z
day: '21'
doi: 10.1103/PhysRevLett.108.214502
extern: 1
intvolume: ' 108'
issue: '21'
month: '05'
publication: Physical Review Letters
publication_status: published
publisher: American Physical Society
publist_id: '4086'
quality_controlled: 0
status: public
title: Edge state in pipe flow experiments
type: journal_article
volume: 108
year: '2012'
...
---
_id: '2804'
abstract:
- lang: eng
text: The analysis of the size distribution of droplets condensing on a substrate
(breath figures) is a test ground for scaling theories. Here, we show that a faithful
description of these distributions must explicitly deal with the growth mechanisms
of the droplets. This finding establishes a gateway connecting nucleation and
growth of the smallest droplets on surfaces to gross features of the evolution
of the droplet size distribution
author:
- first_name: Johannes
full_name: Blaschke, Johannes
last_name: Blaschke
- first_name: Tobias
full_name: Lapp, Tobias
last_name: Lapp
- first_name: Björn
full_name: Björn Hof
id: 3A374330-F248-11E8-B48F-1D18A9856A87
last_name: Hof
orcid: 0000-0003-2057-2754
- first_name: Jürgen
full_name: Vollmer, Jürgen T
last_name: Vollmer
citation:
ama: 'Blaschke J, Lapp T, Hof B, Vollmer J. Breath figures: Nucleation, growth,
coalescence, and the size distribution of droplets. Physical Review Letters.
2012;109(6). doi:10.1103/PhysRevLett.109.068701'
apa: 'Blaschke, J., Lapp, T., Hof, B., & Vollmer, J. (2012). Breath figures:
Nucleation, growth, coalescence, and the size distribution of droplets. Physical
Review Letters. American Physical Society. https://doi.org/10.1103/PhysRevLett.109.068701'
chicago: 'Blaschke, Johannes, Tobias Lapp, Björn Hof, and Jürgen Vollmer. “Breath
Figures: Nucleation, Growth, Coalescence, and the Size Distribution of Droplets.”
Physical Review Letters. American Physical Society, 2012. https://doi.org/10.1103/PhysRevLett.109.068701.'
ieee: 'J. Blaschke, T. Lapp, B. Hof, and J. Vollmer, “Breath figures: Nucleation,
growth, coalescence, and the size distribution of droplets,” Physical Review
Letters, vol. 109, no. 6. American Physical Society, 2012.'
ista: 'Blaschke J, Lapp T, Hof B, Vollmer J. 2012. Breath figures: Nucleation, growth,
coalescence, and the size distribution of droplets. Physical Review Letters. 109(6).'
mla: 'Blaschke, Johannes, et al. “Breath Figures: Nucleation, Growth, Coalescence,
and the Size Distribution of Droplets.” Physical Review Letters, vol. 109,
no. 6, American Physical Society, 2012, doi:10.1103/PhysRevLett.109.068701.'
short: J. Blaschke, T. Lapp, B. Hof, J. Vollmer, Physical Review Letters 109 (2012).
date_created: 2018-12-11T11:59:41Z
date_published: 2012-08-10T00:00:00Z
date_updated: 2021-01-12T06:59:50Z
day: '10'
doi: 10.1103/PhysRevLett.109.068701
extern: 1
intvolume: ' 109'
issue: '6'
month: '08'
publication: Physical Review Letters
publication_status: published
publisher: American Physical Society
publist_id: '4085'
quality_controlled: 0
status: public
title: 'Breath figures: Nucleation, growth, coalescence, and the size distribution
of droplets'
type: journal_article
volume: 109
year: '2012'
...