---
_id: '9550'
abstract:
- lang: eng
  text: 'We prove that the energy of any eigenvector of a sum of several independent
    large Wigner matrices is equally distributed among these matrices with very high
    precision. This shows a particularly strong microcanonical form of the equipartition
    principle for quantum systems whose components are modelled by Wigner matrices. '
acknowledgement: The first author is supported in part by Hong Kong RGC Grant GRF
  16301519 and NSFC 11871425. The second author is supported in part by ERC Advanced
  Grant RANMAT 338804. The third author is supported in part by Swedish Research Council
  Grant VR-2017-05195 and the Knut and Alice Wallenberg Foundation
article_number: e44
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Zhigang
  full_name: Bao, Zhigang
  id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
  last_name: Bao
  orcid: 0000-0003-3036-1475
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Kevin
  full_name: Schnelli, Kevin
  id: 434AD0AE-F248-11E8-B48F-1D18A9856A87
  last_name: Schnelli
  orcid: 0000-0003-0954-3231
citation:
  ama: Bao Z, Erdös L, Schnelli K. Equipartition principle for Wigner matrices. <i>Forum
    of Mathematics, Sigma</i>. 2021;9. doi:<a href="https://doi.org/10.1017/fms.2021.38">10.1017/fms.2021.38</a>
  apa: Bao, Z., Erdös, L., &#38; Schnelli, K. (2021). Equipartition principle for
    Wigner matrices. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press.
    <a href="https://doi.org/10.1017/fms.2021.38">https://doi.org/10.1017/fms.2021.38</a>
  chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Equipartition Principle
    for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>. Cambridge University
    Press, 2021. <a href="https://doi.org/10.1017/fms.2021.38">https://doi.org/10.1017/fms.2021.38</a>.
  ieee: Z. Bao, L. Erdös, and K. Schnelli, “Equipartition principle for Wigner matrices,”
    <i>Forum of Mathematics, Sigma</i>, vol. 9. Cambridge University Press, 2021.
  ista: Bao Z, Erdös L, Schnelli K. 2021. Equipartition principle for Wigner matrices.
    Forum of Mathematics, Sigma. 9, e44.
  mla: Bao, Zhigang, et al. “Equipartition Principle for Wigner Matrices.” <i>Forum
    of Mathematics, Sigma</i>, vol. 9, e44, Cambridge University Press, 2021, doi:<a
    href="https://doi.org/10.1017/fms.2021.38">10.1017/fms.2021.38</a>.
  short: Z. Bao, L. Erdös, K. Schnelli, Forum of Mathematics, Sigma 9 (2021).
date_created: 2021-06-13T22:01:33Z
date_published: 2021-05-27T00:00:00Z
date_updated: 2023-08-08T14:03:40Z
day: '27'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1017/fms.2021.38
ec_funded: 1
external_id:
  arxiv:
  - '2008.07061'
  isi:
  - '000654960800001'
file:
- access_level: open_access
  checksum: 47c986578de132200d41e6d391905519
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  creator: cziletti
  date_created: 2021-06-15T14:40:45Z
  date_updated: 2021-06-15T14:40:45Z
  file_id: '9555'
  file_name: 2021_ForumMath_Bao.pdf
  file_size: 483458
  relation: main_file
  success: 1
file_date_updated: 2021-06-15T14:40:45Z
has_accepted_license: '1'
intvolume: '         9'
isi: 1
language:
- iso: eng
month: '05'
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'
scopus_import: '1'
status: public
title: Equipartition principle for Wigner 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 9
year: '2021'
...
---
_id: '10862'
abstract:
- lang: eng
  text: We consider the sum of two large Hermitian matrices A and B with a Haar unitary
    conjugation bringing them into a general relative position. We prove that the
    eigenvalue density on the scale slightly above the local eigenvalue spacing is
    asymptotically given by the free additive convolution of the laws of A and B as
    the dimension of the matrix increases. This implies optimal rigidity of the eigenvalues
    and optimal rate of convergence in Voiculescu's theorem. Our previous works [4],
    [5] established these results in the bulk spectrum, the current paper completely
    settles the problem at the spectral edges provided they have the typical square-root
    behavior. The key element of our proof is to compensate the deterioration of the
    stability of the subordination equations by sharp error estimates that properly
    account for the local density near the edge. Our results also hold if the Haar
    unitary matrix is replaced by the Haar orthogonal matrix.
acknowledgement: Partially supported by ERC Advanced Grant RANMAT No. 338804.
article_number: '108639'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Zhigang
  full_name: Bao, Zhigang
  id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
  last_name: Bao
  orcid: 0000-0003-3036-1475
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Kevin
  full_name: Schnelli, Kevin
  last_name: Schnelli
citation:
  ama: Bao Z, Erdös L, Schnelli K. Spectral rigidity for addition of random matrices
    at the regular edge. <i>Journal of Functional Analysis</i>. 2020;279(7). doi:<a
    href="https://doi.org/10.1016/j.jfa.2020.108639">10.1016/j.jfa.2020.108639</a>
  apa: Bao, Z., Erdös, L., &#38; Schnelli, K. (2020). Spectral rigidity for addition
    of random matrices at the regular edge. <i>Journal of Functional Analysis</i>.
    Elsevier. <a href="https://doi.org/10.1016/j.jfa.2020.108639">https://doi.org/10.1016/j.jfa.2020.108639</a>
  chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Spectral Rigidity for
    Addition of Random Matrices at the Regular Edge.” <i>Journal of Functional Analysis</i>.
    Elsevier, 2020. <a href="https://doi.org/10.1016/j.jfa.2020.108639">https://doi.org/10.1016/j.jfa.2020.108639</a>.
  ieee: Z. Bao, L. Erdös, and K. Schnelli, “Spectral rigidity for addition of random
    matrices at the regular edge,” <i>Journal of Functional Analysis</i>, vol. 279,
    no. 7. Elsevier, 2020.
  ista: Bao Z, Erdös L, Schnelli K. 2020. Spectral rigidity for addition of random
    matrices at the regular edge. Journal of Functional Analysis. 279(7), 108639.
  mla: Bao, Zhigang, et al. “Spectral Rigidity for Addition of Random Matrices at
    the Regular Edge.” <i>Journal of Functional Analysis</i>, vol. 279, no. 7, 108639,
    Elsevier, 2020, doi:<a href="https://doi.org/10.1016/j.jfa.2020.108639">10.1016/j.jfa.2020.108639</a>.
  short: Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 279 (2020).
date_created: 2022-03-18T10:18:59Z
date_published: 2020-10-15T00:00:00Z
date_updated: 2023-08-24T14:08:42Z
day: '15'
department:
- _id: LaEr
doi: 10.1016/j.jfa.2020.108639
ec_funded: 1
external_id:
  arxiv:
  - '1708.01597'
  isi:
  - '000559623200009'
intvolume: '       279'
isi: 1
issue: '7'
keyword:
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1708.01597
month: '10'
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:
  issn:
  - 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Spectral rigidity for addition of random matrices at the regular edge
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 279
year: '2020'
...
---
_id: '9104'
abstract:
- lang: eng
  text: We consider the free additive convolution of two probability measures μ and
    ν on the real line and show that μ ⊞ v is supported on a single interval if μ
    and ν each has single interval support. Moreover, the density of μ ⊞ ν is proven
    to vanish as a square root near the edges of its support if both μ and ν have
    power law behavior with exponents between −1 and 1 near their edges. In particular,
    these results show the ubiquity of the conditions in our recent work on optimal
    local law at the spectral edges for addition of random matrices [5].
acknowledgement: "Supported in part by Hong Kong RGC Grant ECS 26301517.\r\nSupported
  in part by ERC Advanced Grant RANMAT No. 338804.\r\nSupported in part by the Knut
  and Alice Wallenberg Foundation and the Swedish Research Council Grant VR-2017-05195."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Zhigang
  full_name: Bao, Zhigang
  id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
  last_name: Bao
  orcid: 0000-0003-3036-1475
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Kevin
  full_name: Schnelli, Kevin
  id: 434AD0AE-F248-11E8-B48F-1D18A9856A87
  last_name: Schnelli
  orcid: 0000-0003-0954-3231
citation:
  ama: Bao Z, Erdös L, Schnelli K. On the support of the free additive convolution.
    <i>Journal d’Analyse Mathematique</i>. 2020;142:323-348. doi:<a href="https://doi.org/10.1007/s11854-020-0135-2">10.1007/s11854-020-0135-2</a>
  apa: Bao, Z., Erdös, L., &#38; Schnelli, K. (2020). On the support of the free additive
    convolution. <i>Journal d’Analyse Mathematique</i>. Springer Nature. <a href="https://doi.org/10.1007/s11854-020-0135-2">https://doi.org/10.1007/s11854-020-0135-2</a>
  chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “On the Support of the
    Free Additive Convolution.” <i>Journal d’Analyse Mathematique</i>. Springer Nature,
    2020. <a href="https://doi.org/10.1007/s11854-020-0135-2">https://doi.org/10.1007/s11854-020-0135-2</a>.
  ieee: Z. Bao, L. Erdös, and K. Schnelli, “On the support of the free additive convolution,”
    <i>Journal d’Analyse Mathematique</i>, vol. 142. Springer Nature, pp. 323–348,
    2020.
  ista: Bao Z, Erdös L, Schnelli K. 2020. On the support of the free additive convolution.
    Journal d’Analyse Mathematique. 142, 323–348.
  mla: Bao, Zhigang, et al. “On the Support of the Free Additive Convolution.” <i>Journal
    d’Analyse Mathematique</i>, vol. 142, Springer Nature, 2020, pp. 323–48, doi:<a
    href="https://doi.org/10.1007/s11854-020-0135-2">10.1007/s11854-020-0135-2</a>.
  short: Z. Bao, L. Erdös, K. Schnelli, Journal d’Analyse Mathematique 142 (2020)
    323–348.
date_created: 2021-02-07T23:01:15Z
date_published: 2020-11-01T00:00:00Z
date_updated: 2023-08-24T11:16:03Z
day: '01'
department:
- _id: LaEr
doi: 10.1007/s11854-020-0135-2
ec_funded: 1
external_id:
  arxiv:
  - '1804.11199'
  isi:
  - '000611879400008'
intvolume: '       142'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1804.11199
month: '11'
oa: 1
oa_version: Preprint
page: 323-348
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
publication: Journal d'Analyse Mathematique
publication_identifier:
  eissn:
  - '15658538'
  issn:
  - '00217670'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the support of the free additive convolution
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 142
year: '2020'
...
---
_id: '6511'
abstract:
- lang: eng
  text: Let U and V be two independent N by N random matrices that are distributed
    according to Haar measure on U(N). Let Σ be a nonnegative deterministic N by N
    matrix. The single ring theorem [Ann. of Math. (2) 174 (2011) 1189–1217] asserts
    that the empirical eigenvalue distribution of the matrix X:=UΣV∗ converges weakly,
    in the limit of large N, to a deterministic measure which is supported on a single
    ring centered at the origin in ℂ. Within the bulk regime, that is, in the interior
    of the single ring, we establish the convergence of the empirical eigenvalue distribution
    on the optimal local scale of order N−1/2+ε and establish the optimal convergence
    rate. The same results hold true when U and V are Haar distributed on O(N).
article_processing_charge: No
arxiv: 1
author:
- first_name: Zhigang
  full_name: Bao, Zhigang
  id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
  last_name: Bao
  orcid: 0000-0003-3036-1475
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Kevin
  full_name: Schnelli, Kevin
  id: 434AD0AE-F248-11E8-B48F-1D18A9856A87
  last_name: Schnelli
  orcid: 0000-0003-0954-3231
citation:
  ama: Bao Z, Erdös L, Schnelli K. Local single ring theorem on optimal scale. <i>Annals
    of Probability</i>. 2019;47(3):1270-1334. doi:<a href="https://doi.org/10.1214/18-AOP1284">10.1214/18-AOP1284</a>
  apa: Bao, Z., Erdös, L., &#38; Schnelli, K. (2019). Local single ring theorem on
    optimal scale. <i>Annals of Probability</i>. Institute of Mathematical Statistics.
    <a href="https://doi.org/10.1214/18-AOP1284">https://doi.org/10.1214/18-AOP1284</a>
  chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Single Ring Theorem
    on Optimal Scale.” <i>Annals of Probability</i>. Institute of Mathematical Statistics,
    2019. <a href="https://doi.org/10.1214/18-AOP1284">https://doi.org/10.1214/18-AOP1284</a>.
  ieee: Z. Bao, L. Erdös, and K. Schnelli, “Local single ring theorem on optimal scale,”
    <i>Annals of Probability</i>, vol. 47, no. 3. Institute of Mathematical Statistics,
    pp. 1270–1334, 2019.
  ista: Bao Z, Erdös L, Schnelli K. 2019. Local single ring theorem on optimal scale.
    Annals of Probability. 47(3), 1270–1334.
  mla: Bao, Zhigang, et al. “Local Single Ring Theorem on Optimal Scale.” <i>Annals
    of Probability</i>, vol. 47, no. 3, Institute of Mathematical Statistics, 2019,
    pp. 1270–334, doi:<a href="https://doi.org/10.1214/18-AOP1284">10.1214/18-AOP1284</a>.
  short: Z. Bao, L. Erdös, K. Schnelli, Annals of Probability 47 (2019) 1270–1334.
date_created: 2019-06-02T21:59:13Z
date_published: 2019-05-01T00:00:00Z
date_updated: 2023-08-28T09:32:29Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/18-AOP1284
ec_funded: 1
external_id:
  arxiv:
  - '1612.05920'
  isi:
  - '000466616100003'
intvolume: '        47'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1612.05920
month: '05'
oa: 1
oa_version: Preprint
page: 1270-1334
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:
  - '00911798'
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local single ring theorem on optimal scale
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 47
year: '2019'
...
---
_id: '733'
abstract:
- lang: eng
  text: Let A and B be two N by N deterministic Hermitian matrices and let U be an
    N by N Haar distributed unitary matrix. It is well known that the spectral distribution
    of the sum H = A + UBU∗ converges weakly to the free additive convolution of the
    spectral distributions of A and B, as N tends to infinity. We establish the optimal
    convergence rate in the bulk of the spectrum.
acknowledgement: Partially supported by ERC Advanced Grant RANMAT No. 338804, Hong
  Kong RGC grant ECS 26301517, and the Göran Gustafsson Foundation
article_processing_charge: No
author:
- first_name: Zhigang
  full_name: Bao, Zhigang
  id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
  last_name: Bao
  orcid: 0000-0003-3036-1475
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Kevin
  full_name: Schnelli, Kevin
  id: 434AD0AE-F248-11E8-B48F-1D18A9856A87
  last_name: Schnelli
  orcid: 0000-0003-0954-3231
citation:
  ama: Bao Z, Erdös L, Schnelli K. Convergence rate for spectral distribution of addition
    of random matrices. <i>Advances in Mathematics</i>. 2017;319:251-291. doi:<a href="https://doi.org/10.1016/j.aim.2017.08.028">10.1016/j.aim.2017.08.028</a>
  apa: Bao, Z., Erdös, L., &#38; Schnelli, K. (2017). Convergence rate for spectral
    distribution of addition of random matrices. <i>Advances in Mathematics</i>. Academic
    Press. <a href="https://doi.org/10.1016/j.aim.2017.08.028">https://doi.org/10.1016/j.aim.2017.08.028</a>
  chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Convergence Rate for Spectral
    Distribution of Addition of Random Matrices.” <i>Advances in Mathematics</i>.
    Academic Press, 2017. <a href="https://doi.org/10.1016/j.aim.2017.08.028">https://doi.org/10.1016/j.aim.2017.08.028</a>.
  ieee: Z. Bao, L. Erdös, and K. Schnelli, “Convergence rate for spectral distribution
    of addition of random matrices,” <i>Advances in Mathematics</i>, vol. 319. Academic
    Press, pp. 251–291, 2017.
  ista: Bao Z, Erdös L, Schnelli K. 2017. Convergence rate for spectral distribution
    of addition of random matrices. Advances in Mathematics. 319, 251–291.
  mla: Bao, Zhigang, et al. “Convergence Rate for Spectral Distribution of Addition
    of Random Matrices.” <i>Advances in Mathematics</i>, vol. 319, Academic Press,
    2017, pp. 251–91, doi:<a href="https://doi.org/10.1016/j.aim.2017.08.028">10.1016/j.aim.2017.08.028</a>.
  short: Z. Bao, L. Erdös, K. Schnelli, Advances in Mathematics 319 (2017) 251–291.
date_created: 2018-12-11T11:48:13Z
date_published: 2017-10-15T00:00:00Z
date_updated: 2023-09-28T11:30:42Z
day: '15'
department:
- _id: LaEr
doi: 10.1016/j.aim.2017.08.028
ec_funded: 1
external_id:
  isi:
  - '000412150400010'
intvolume: '       319'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1606.03076
month: '10'
oa: 1
oa_version: Submitted Version
page: 251 - 291
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
publication: Advances in Mathematics
publication_status: published
publisher: Academic Press
publist_id: '6935'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Convergence rate for spectral distribution of addition of random matrices
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 319
year: '2017'
...
---
_id: '1528'
abstract:
- lang: eng
  text: 'We consider N×N Hermitian random matrices H consisting of blocks of size
    M≥N6/7. The matrix elements are i.i.d. within the blocks, close to a Gaussian
    in the four moment matching sense, but their distribution varies from block to
    block to form a block-band structure, with an essential band width M. We show
    that the entries of the Green’s function G(z)=(H−z)−1 satisfy the local semicircle
    law with spectral parameter z=E+iη down to the real axis for any η≫N−1, using
    a combination of the supersymmetry method inspired by Shcherbina (J Stat Phys
    155(3): 466–499, 2014) and the Green’s function comparison strategy. Previous
    estimates were valid only for η≫M−1. The new estimate also implies that the eigenvectors
    in the middle of the spectrum are fully delocalized.'
acknowledgement: "Z. Bao was supported by ERC Advanced Grant RANMAT No. 338804; L.
  Erdős was partially supported by ERC Advanced Grant RANMAT No. 338804.\r\nOpen access
  funding provided by Institute of Science and Technology (IST Austria). The authors
  are very grateful to the anonymous referees for careful reading and valuable comments,
  which helped to improve the organization."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Zhigang
  full_name: Bao, Zhigang
  id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
  last_name: Bao
  orcid: 0000-0003-3036-1475
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
citation:
  ama: Bao Z, Erdös L. Delocalization for a class of random block band matrices. <i>Probability
    Theory and Related Fields</i>. 2017;167(3-4):673-776. doi:<a href="https://doi.org/10.1007/s00440-015-0692-y">10.1007/s00440-015-0692-y</a>
  apa: Bao, Z., &#38; Erdös, L. (2017). Delocalization for a class of random block
    band matrices. <i>Probability Theory and Related Fields</i>. Springer. <a href="https://doi.org/10.1007/s00440-015-0692-y">https://doi.org/10.1007/s00440-015-0692-y</a>
  chicago: Bao, Zhigang, and László Erdös. “Delocalization for a Class of Random Block
    Band Matrices.” <i>Probability Theory and Related Fields</i>. Springer, 2017.
    <a href="https://doi.org/10.1007/s00440-015-0692-y">https://doi.org/10.1007/s00440-015-0692-y</a>.
  ieee: Z. Bao and L. Erdös, “Delocalization for a class of random block band matrices,”
    <i>Probability Theory and Related Fields</i>, vol. 167, no. 3–4. Springer, pp.
    673–776, 2017.
  ista: Bao Z, Erdös L. 2017. Delocalization for a class of random block band matrices.
    Probability Theory and Related Fields. 167(3–4), 673–776.
  mla: Bao, Zhigang, and László Erdös. “Delocalization for a Class of Random Block
    Band Matrices.” <i>Probability Theory and Related Fields</i>, vol. 167, no. 3–4,
    Springer, 2017, pp. 673–776, doi:<a href="https://doi.org/10.1007/s00440-015-0692-y">10.1007/s00440-015-0692-y</a>.
  short: Z. Bao, L. Erdös, Probability Theory and Related Fields 167 (2017) 673–776.
date_created: 2018-12-11T11:52:32Z
date_published: 2017-04-01T00:00:00Z
date_updated: 2023-09-20T09:42:12Z
day: '01'
ddc:
- '530'
department:
- _id: LaEr
doi: 10.1007/s00440-015-0692-y
ec_funded: 1
external_id:
  isi:
  - '000398842700004'
file:
- access_level: open_access
  checksum: 67afa85ff1e220cbc1f9f477a828513c
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has_accepted_license: '1'
intvolume: '       167'
isi: 1
issue: 3-4
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 673 - 776
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
publication: Probability Theory and Related Fields
publication_identifier:
  issn:
  - '01788051'
publication_status: published
publisher: Springer
publist_id: '5644'
pubrep_id: '489'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Delocalization for a class of random block band 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: 167
year: '2017'
...
---
_id: '1207'
abstract:
- lang: eng
  text: The eigenvalue distribution of the sum of two large Hermitian matrices, when
    one of them is conjugated by a Haar distributed unitary matrix, is asymptotically
    given by the free convolution of their spectral distributions. We prove that this
    convergence also holds locally in the bulk of the spectrum, down to the optimal
    scales larger than the eigenvalue spacing. The corresponding eigenvectors are
    fully delocalized. Similar results hold for the sum of two real symmetric matrices,
    when one is conjugated by Haar orthogonal matrix.
article_processing_charge: Yes (via OA deal)
author:
- first_name: Zhigang
  full_name: Bao, Zhigang
  id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
  last_name: Bao
  orcid: 0000-0003-3036-1475
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Kevin
  full_name: Schnelli, Kevin
  id: 434AD0AE-F248-11E8-B48F-1D18A9856A87
  last_name: Schnelli
  orcid: 0000-0003-0954-3231
citation:
  ama: Bao Z, Erdös L, Schnelli K. Local law of addition of random matrices on optimal
    scale. <i>Communications in Mathematical Physics</i>. 2017;349(3):947-990. doi:<a
    href="https://doi.org/10.1007/s00220-016-2805-6">10.1007/s00220-016-2805-6</a>
  apa: Bao, Z., Erdös, L., &#38; Schnelli, K. (2017). Local law of addition of random
    matrices on optimal scale. <i>Communications in Mathematical Physics</i>. Springer.
    <a href="https://doi.org/10.1007/s00220-016-2805-6">https://doi.org/10.1007/s00220-016-2805-6</a>
  chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Law of Addition
    of Random Matrices on Optimal Scale.” <i>Communications in Mathematical Physics</i>.
    Springer, 2017. <a href="https://doi.org/10.1007/s00220-016-2805-6">https://doi.org/10.1007/s00220-016-2805-6</a>.
  ieee: Z. Bao, L. Erdös, and K. Schnelli, “Local law of addition of random matrices
    on optimal scale,” <i>Communications in Mathematical Physics</i>, vol. 349, no.
    3. Springer, pp. 947–990, 2017.
  ista: Bao Z, Erdös L, Schnelli K. 2017. Local law of addition of random matrices
    on optimal scale. Communications in Mathematical Physics. 349(3), 947–990.
  mla: Bao, Zhigang, et al. “Local Law of Addition of Random Matrices on Optimal Scale.”
    <i>Communications in Mathematical Physics</i>, vol. 349, no. 3, Springer, 2017,
    pp. 947–90, doi:<a href="https://doi.org/10.1007/s00220-016-2805-6">10.1007/s00220-016-2805-6</a>.
  short: Z. Bao, L. Erdös, K. Schnelli, Communications in Mathematical Physics 349
    (2017) 947–990.
date_created: 2018-12-11T11:50:43Z
date_published: 2017-02-01T00:00:00Z
date_updated: 2023-09-20T11:16:57Z
day: '01'
ddc:
- '530'
department:
- _id: LaEr
doi: 10.1007/s00220-016-2805-6
ec_funded: 1
external_id:
  isi:
  - '000393696700005'
file:
- access_level: open_access
  checksum: ddff79154c3daf27237de5383b1264a9
  content_type: application/pdf
  creator: system
  date_created: 2018-12-12T10:14:47Z
  date_updated: 2020-07-14T12:44:39Z
  file_id: '5102'
  file_name: IST-2016-722-v1+1_s00220-016-2805-6.pdf
  file_size: 1033743
  relation: main_file
file_date_updated: 2020-07-14T12:44:39Z
has_accepted_license: '1'
intvolume: '       349'
isi: 1
issue: '3'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 947 - 990
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
publication: Communications in Mathematical Physics
publication_identifier:
  issn:
  - '00103616'
publication_status: published
publisher: Springer
publist_id: '6141'
pubrep_id: '722'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local law of addition of random matrices on optimal scale
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: 349
year: '2017'
...
---
_id: '1434'
abstract:
- lang: eng
  text: We prove that the system of subordination equations, defining the free additive
    convolution of two probability measures, is stable away from the edges of the
    support and blow-up singularities by showing that the recent smoothness condition
    of Kargin is always satisfied. As an application, we consider the local spectral
    statistics of the random matrix ensemble A+UBU⁎A+UBU⁎, where U is a Haar distributed
    random unitary or orthogonal matrix, and A and B   are deterministic matrices.
    In the bulk regime, we prove that the empirical spectral distribution of A+UBU⁎A+UBU⁎
    concentrates around the free additive convolution of the spectral distributions
    of A and B   on scales down to N−2/3N−2/3.
author:
- first_name: Zhigang
  full_name: Bao, Zhigang
  id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
  last_name: Bao
  orcid: 0000-0003-3036-1475
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Kevin
  full_name: Schnelli, Kevin
  id: 434AD0AE-F248-11E8-B48F-1D18A9856A87
  last_name: Schnelli
  orcid: 0000-0003-0954-3231
citation:
  ama: Bao Z, Erdös L, Schnelli K. Local stability of the free additive convolution.
    <i>Journal of Functional Analysis</i>. 2016;271(3):672-719. doi:<a href="https://doi.org/10.1016/j.jfa.2016.04.006">10.1016/j.jfa.2016.04.006</a>
  apa: Bao, Z., Erdös, L., &#38; Schnelli, K. (2016). Local stability of the free
    additive convolution. <i>Journal of Functional Analysis</i>. Academic Press. <a
    href="https://doi.org/10.1016/j.jfa.2016.04.006">https://doi.org/10.1016/j.jfa.2016.04.006</a>
  chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Stability of the
    Free Additive Convolution.” <i>Journal of Functional Analysis</i>. Academic Press,
    2016. <a href="https://doi.org/10.1016/j.jfa.2016.04.006">https://doi.org/10.1016/j.jfa.2016.04.006</a>.
  ieee: Z. Bao, L. Erdös, and K. Schnelli, “Local stability of the free additive convolution,”
    <i>Journal of Functional Analysis</i>, vol. 271, no. 3. Academic Press, pp. 672–719,
    2016.
  ista: Bao Z, Erdös L, Schnelli K. 2016. Local stability of the free additive convolution.
    Journal of Functional Analysis. 271(3), 672–719.
  mla: Bao, Zhigang, et al. “Local Stability of the Free Additive Convolution.” <i>Journal
    of Functional Analysis</i>, vol. 271, no. 3, Academic Press, 2016, pp. 672–719,
    doi:<a href="https://doi.org/10.1016/j.jfa.2016.04.006">10.1016/j.jfa.2016.04.006</a>.
  short: Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 271 (2016)
    672–719.
date_created: 2018-12-11T11:52:00Z
date_published: 2016-08-01T00:00:00Z
date_updated: 2021-01-12T06:50:42Z
day: '01'
department:
- _id: LaEr
doi: 10.1016/j.jfa.2016.04.006
ec_funded: 1
intvolume: '       271'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1508.05905
month: '08'
oa: 1
oa_version: Preprint
page: 672 - 719
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_status: published
publisher: Academic Press
publist_id: '5764'
quality_controlled: '1'
scopus_import: 1
status: public
title: Local stability of the free additive convolution
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 271
year: '2016'
...
---
_id: '1504'
abstract:
- lang: eng
  text: Let Q = (Q1, . . . , Qn) be a random vector drawn from the uniform distribution
    on the set of all n! permutations of {1, 2, . . . , n}. Let Z = (Z1, . . . , Zn),
    where Zj is the mean zero variance one random variable obtained by centralizing
    and normalizing Qj , j = 1, . . . , n. Assume that Xi , i = 1, . . . ,p are i.i.d.
    copies of 1/√ p Z and X = Xp,n is the p × n random matrix with Xi as its ith row.
    Then Sn = XX is called the p × n Spearman's rank correlation matrix which can
    be regarded as a high dimensional extension of the classical nonparametric statistic
    Spearman's rank correlation coefficient between two independent random variables.
    In this paper, we establish a CLT for the linear spectral statistics of this nonparametric
    random matrix model in the scenario of high dimension, namely, p = p(n) and p/n→c
    ∈ (0,∞) as n→∞.We propose a novel evaluation scheme to estimate the core quantity
    in Anderson and Zeitouni's cumulant method in [Ann. Statist. 36 (2008) 2553-2576]
    to bypass the so-called joint cumulant summability. In addition, we raise a two-step
    comparison approach to obtain the explicit formulae for the mean and covariance
    functions in the CLT. Relying on this CLT, we then construct a distribution-free
    statistic to test complete independence for components of random vectors. Owing
    to the nonparametric property, we can use this test on generally distributed random
    variables including the heavy-tailed ones.
author:
- first_name: Zhigang
  full_name: Bao, Zhigang
  id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
  last_name: Bao
  orcid: 0000-0003-3036-1475
- first_name: Liang
  full_name: Lin, Liang
  last_name: Lin
- first_name: Guangming
  full_name: Pan, Guangming
  last_name: Pan
- first_name: Wang
  full_name: Zhou, Wang
  last_name: Zhou
citation:
  ama: Bao Z, Lin L, Pan G, Zhou W. Spectral statistics of large dimensional spearman
    s rank correlation matrix and its application. <i>Annals of Statistics</i>. 2015;43(6):2588-2623.
    doi:<a href="https://doi.org/10.1214/15-AOS1353">10.1214/15-AOS1353</a>
  apa: Bao, Z., Lin, L., Pan, G., &#38; Zhou, W. (2015). Spectral statistics of large
    dimensional spearman s rank correlation matrix and its application. <i>Annals
    of Statistics</i>. Institute of Mathematical Statistics. <a href="https://doi.org/10.1214/15-AOS1353">https://doi.org/10.1214/15-AOS1353</a>
  chicago: Bao, Zhigang, Liang Lin, Guangming Pan, and Wang Zhou. “Spectral Statistics
    of Large Dimensional Spearman s Rank Correlation Matrix and Its Application.”
    <i>Annals of Statistics</i>. Institute of Mathematical Statistics, 2015. <a href="https://doi.org/10.1214/15-AOS1353">https://doi.org/10.1214/15-AOS1353</a>.
  ieee: Z. Bao, L. Lin, G. Pan, and W. Zhou, “Spectral statistics of large dimensional
    spearman s rank correlation matrix and its application,” <i>Annals of Statistics</i>,
    vol. 43, no. 6. Institute of Mathematical Statistics, pp. 2588–2623, 2015.
  ista: Bao Z, Lin L, Pan G, Zhou W. 2015. Spectral statistics of large dimensional
    spearman s rank correlation matrix and its application. Annals of Statistics.
    43(6), 2588–2623.
  mla: Bao, Zhigang, et al. “Spectral Statistics of Large Dimensional Spearman s Rank
    Correlation Matrix and Its Application.” <i>Annals of Statistics</i>, vol. 43,
    no. 6, Institute of Mathematical Statistics, 2015, pp. 2588–623, doi:<a href="https://doi.org/10.1214/15-AOS1353">10.1214/15-AOS1353</a>.
  short: Z. Bao, L. Lin, G. Pan, W. Zhou, Annals of Statistics 43 (2015) 2588–2623.
date_created: 2018-12-11T11:52:24Z
date_published: 2015-12-01T00:00:00Z
date_updated: 2021-01-12T06:51:14Z
day: '01'
doi: 10.1214/15-AOS1353
extern: '1'
intvolume: '        43'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1312.5119
month: '12'
oa: 1
oa_version: Published Version
page: 2588 - 2623
publication: Annals of Statistics
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '5674'
quality_controlled: '1'
status: public
title: Spectral statistics of large dimensional spearman s rank correlation matrix
  and its application
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 43
year: '2015'
...
---
_id: '1505'
abstract:
- lang: eng
  text: This paper is aimed at deriving the universality of the largest eigenvalue
    of a class of high-dimensional real or complex sample covariance matrices of the
    form W N =Σ 1/2XX∗Σ 1/2 . Here, X = (xij )M,N is an M× N random matrix with independent
    entries xij , 1 ≤ i M,≤ 1 ≤ j ≤ N such that Exij = 0, E|xij |2 = 1/N . On dimensionality,
    we assume that M = M(N) and N/M → d ε (0, ∞) as N ∞→. For a class of general deterministic
    positive-definite M × M matrices Σ , under some additional assumptions on the
    distribution of xij 's, we show that the limiting behavior of the largest eigenvalue
    of W N is universal, via pursuing a Green function comparison strategy raised
    in [Probab. Theory Related Fields 154 (2012) 341-407, Adv. Math. 229 (2012) 1435-1515]
    by Erd″os, Yau and Yin for Wigner matrices and extended by Pillai and Yin [Ann.
    Appl. Probab. 24 (2014) 935-1001] to sample covariance matrices in the null case
    (&amp;Epsi = I ). Consequently, in the standard complex case (Ex2 ij = 0), combing
    this universality property and the results known for Gaussian matrices obtained
    by El Karoui in [Ann. Probab. 35 (2007) 663-714] (nonsingular case) and Onatski
    in [Ann. Appl. Probab. 18 (2008) 470-490] (singular case), we show that after
    an appropriate normalization the largest eigenvalue of W N converges weakly to
    the type 2 Tracy-Widom distribution TW2 . Moreover, in the real case, we show
    that whenΣ is spiked with a fixed number of subcritical spikes, the type 1 Tracy-Widom
    limit TW1 holds for the normalized largest eigenvalue of W N , which extends a
    result of Féral and Péché in [J. Math. Phys. 50 (2009) 073302] to the scenario
    of nondiagonal Σ and more generally distributed X . In summary, we establish the
    Tracy-Widom type universality for the largest eigenvalue of generally distributed
    sample covariance matrices under quite light assumptions on &amp;Sigma . Applications
    of these limiting results to statistical signal detection and structure recognition
    of separable covariance matrices are also discussed.
acknowledgement: "B.Z. was supported  in  part  by  NSFC  Grant  11071213,  ZJNSF
  \ Grant  R6090034  and  SRFDP  Grant 20100101110001. P.G. was supported in part
  by the Ministry of Education, Singapore, under Grant ARC 14/11. Z.W. was supported
  \ in  part  by  the  Ministry  of  Education,  Singapore,  under  Grant  ARC  14/11,
  \ and  by a Grant R-155-000-131-112 at the National University of Singapore\r\n"
author:
- first_name: Zhigang
  full_name: Bao, Zhigang
  id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
  last_name: Bao
  orcid: 0000-0003-3036-1475
- first_name: Guangming
  full_name: Pan, Guangming
  last_name: Pan
- first_name: Wang
  full_name: Zhou, Wang
  last_name: Zhou
citation:
  ama: Bao Z, Pan G, Zhou W. Universality for the largest eigenvalue of sample covariance
    matrices with general population. <i>Annals of Statistics</i>. 2015;43(1):382-421.
    doi:<a href="https://doi.org/10.1214/14-AOS1281">10.1214/14-AOS1281</a>
  apa: Bao, Z., Pan, G., &#38; Zhou, W. (2015). Universality for the largest eigenvalue
    of sample covariance matrices with general population. <i>Annals of Statistics</i>.
    Institute of Mathematical Statistics. <a href="https://doi.org/10.1214/14-AOS1281">https://doi.org/10.1214/14-AOS1281</a>
  chicago: Bao, Zhigang, Guangming Pan, and Wang Zhou. “Universality for the Largest
    Eigenvalue of Sample Covariance Matrices with General Population.” <i>Annals of
    Statistics</i>. Institute of Mathematical Statistics, 2015. <a href="https://doi.org/10.1214/14-AOS1281">https://doi.org/10.1214/14-AOS1281</a>.
  ieee: Z. Bao, G. Pan, and W. Zhou, “Universality for the largest eigenvalue of sample
    covariance matrices with general population,” <i>Annals of Statistics</i>, vol.
    43, no. 1. Institute of Mathematical Statistics, pp. 382–421, 2015.
  ista: Bao Z, Pan G, Zhou W. 2015. Universality for the largest eigenvalue of sample
    covariance matrices with general population. Annals of Statistics. 43(1), 382–421.
  mla: Bao, Zhigang, et al. “Universality for the Largest Eigenvalue of Sample Covariance
    Matrices with General Population.” <i>Annals of Statistics</i>, vol. 43, no. 1,
    Institute of Mathematical Statistics, 2015, pp. 382–421, doi:<a href="https://doi.org/10.1214/14-AOS1281">10.1214/14-AOS1281</a>.
  short: Z. Bao, G. Pan, W. Zhou, Annals of Statistics 43 (2015) 382–421.
date_created: 2018-12-11T11:52:25Z
date_published: 2015-02-01T00:00:00Z
date_updated: 2021-01-12T06:51:14Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/14-AOS1281
intvolume: '        43'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1304.5690
month: '02'
oa: 1
oa_version: Preprint
page: 382 - 421
publication: Annals of Statistics
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '5672'
quality_controlled: '1'
status: public
title: Universality for the largest eigenvalue of sample covariance matrices with
  general population
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 43
year: '2015'
...
---
_id: '1506'
abstract:
- lang: eng
  text: Consider the square random matrix An = (aij)n,n, where {aij:= a(n)ij , i,
    j = 1, . . . , n} is a collection of independent real random variables with means
    zero and variances one. Under the additional moment condition supn max1≤i,j ≤n
    Ea4ij &lt;∞, we prove Girko's logarithmic law of det An in the sense that as n→∞
    log | detAn| ? (1/2) log(n-1)! d/→√(1/2) log n N(0, 1).
author:
- first_name: Zhigang
  full_name: Bao, Zhigang
  id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
  last_name: Bao
  orcid: 0000-0003-3036-1475
- first_name: Guangming
  full_name: Pan, Guangming
  last_name: Pan
- first_name: Wang
  full_name: Zhou, Wang
  last_name: Zhou
citation:
  ama: Bao Z, Pan G, Zhou W. The logarithmic law of random determinant. <i>Bernoulli</i>.
    2015;21(3):1600-1628. doi:<a href="https://doi.org/10.3150/14-BEJ615">10.3150/14-BEJ615</a>
  apa: Bao, Z., Pan, G., &#38; Zhou, W. (2015). The logarithmic law of random determinant.
    <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics and Probability.
    <a href="https://doi.org/10.3150/14-BEJ615">https://doi.org/10.3150/14-BEJ615</a>
  chicago: Bao, Zhigang, Guangming Pan, and Wang Zhou. “The Logarithmic Law of Random
    Determinant.” <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics
    and Probability, 2015. <a href="https://doi.org/10.3150/14-BEJ615">https://doi.org/10.3150/14-BEJ615</a>.
  ieee: Z. Bao, G. Pan, and W. Zhou, “The logarithmic law of random determinant,”
    <i>Bernoulli</i>, vol. 21, no. 3. Bernoulli Society for Mathematical Statistics
    and Probability, pp. 1600–1628, 2015.
  ista: Bao Z, Pan G, Zhou W. 2015. The logarithmic law of random determinant. Bernoulli.
    21(3), 1600–1628.
  mla: Bao, Zhigang, et al. “The Logarithmic Law of Random Determinant.” <i>Bernoulli</i>,
    vol. 21, no. 3, Bernoulli Society for Mathematical Statistics and Probability,
    2015, pp. 1600–28, doi:<a href="https://doi.org/10.3150/14-BEJ615">10.3150/14-BEJ615</a>.
  short: Z. Bao, G. Pan, W. Zhou, Bernoulli 21 (2015) 1600–1628.
date_created: 2018-12-11T11:52:25Z
date_published: 2015-08-01T00:00:00Z
date_updated: 2021-01-12T06:51:14Z
day: '01'
department:
- _id: LaEr
doi: 10.3150/14-BEJ615
intvolume: '        21'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1208.5823
month: '08'
oa: 1
oa_version: Preprint
page: 1600 - 1628
publication: Bernoulli
publication_status: published
publisher: Bernoulli Society for Mathematical Statistics and Probability
publist_id: '5671'
quality_controlled: '1'
status: public
title: The logarithmic law of random determinant
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 21
year: '2015'
...
---
_id: '1585'
abstract:
- lang: eng
  text: In this paper, we consider the fluctuation of mutual information statistics
    of a multiple input multiple output channel communication systems without assuming
    that the entries of the channel matrix have zero pseudovariance. To this end,
    we also establish a central limit theorem of the linear spectral statistics for
    sample covariance matrices under general moment conditions by removing the restrictions
    imposed on the second moment and fourth moment on the matrix entries in Bai and
    Silverstein (2004).
acknowledgement: "G. Pan was supported by MOE Tier 2 under Grant 2014-T2-2-060 and
  in part by Tier 1 under Grant RG25/14 through the Nanyang Technological University,
  Singapore. W. Zhou was supported by the National University of Singapore, Singapore,
  under Grant R-155-000-131-112.\r\n"
author:
- first_name: Zhigang
  full_name: Bao, Zhigang
  id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
  last_name: Bao
  orcid: 0000-0003-3036-1475
- first_name: Guangming
  full_name: Pan, Guangming
  last_name: Pan
- first_name: Wang
  full_name: Zhou, Wang
  last_name: Zhou
citation:
  ama: Bao Z, Pan G, Zhou W. Asymptotic mutual information statistics of MIMO channels
    and CLT of sample covariance matrices. <i>IEEE Transactions on Information Theory</i>.
    2015;61(6):3413-3426. doi:<a href="https://doi.org/10.1109/TIT.2015.2421894">10.1109/TIT.2015.2421894</a>
  apa: Bao, Z., Pan, G., &#38; Zhou, W. (2015). Asymptotic mutual information statistics
    of MIMO channels and CLT of sample covariance matrices. <i>IEEE Transactions on
    Information Theory</i>. IEEE. <a href="https://doi.org/10.1109/TIT.2015.2421894">https://doi.org/10.1109/TIT.2015.2421894</a>
  chicago: Bao, Zhigang, Guangming Pan, and Wang Zhou. “Asymptotic Mutual Information
    Statistics of MIMO Channels and CLT of Sample Covariance Matrices.” <i>IEEE Transactions
    on Information Theory</i>. IEEE, 2015. <a href="https://doi.org/10.1109/TIT.2015.2421894">https://doi.org/10.1109/TIT.2015.2421894</a>.
  ieee: Z. Bao, G. Pan, and W. Zhou, “Asymptotic mutual information statistics of
    MIMO channels and CLT of sample covariance matrices,” <i>IEEE Transactions on
    Information Theory</i>, vol. 61, no. 6. IEEE, pp. 3413–3426, 2015.
  ista: Bao Z, Pan G, Zhou W. 2015. Asymptotic mutual information statistics of MIMO
    channels and CLT of sample covariance matrices. IEEE Transactions on Information
    Theory. 61(6), 3413–3426.
  mla: Bao, Zhigang, et al. “Asymptotic Mutual Information Statistics of MIMO Channels
    and CLT of Sample Covariance Matrices.” <i>IEEE Transactions on Information Theory</i>,
    vol. 61, no. 6, IEEE, 2015, pp. 3413–26, doi:<a href="https://doi.org/10.1109/TIT.2015.2421894">10.1109/TIT.2015.2421894</a>.
  short: Z. Bao, G. Pan, W. Zhou, IEEE Transactions on Information Theory 61 (2015)
    3413–3426.
date_created: 2018-12-11T11:52:52Z
date_published: 2015-06-01T00:00:00Z
date_updated: 2021-01-12T06:51:46Z
day: '01'
department:
- _id: LaEr
doi: 10.1109/TIT.2015.2421894
intvolume: '        61'
issue: '6'
language:
- iso: eng
month: '06'
oa_version: None
page: 3413 - 3426
publication: IEEE Transactions on Information Theory
publication_status: published
publisher: IEEE
publist_id: '5586'
quality_controlled: '1'
scopus_import: 1
status: public
title: Asymptotic mutual information statistics of MIMO channels and CLT of sample
  covariance matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 61
year: '2015'
...