A. Bufetov, S. Mkrtchyan, M. Shcherbina, A. Soshnikov, “Entropy and the Shannon–McMillan–Breiman theorem for beta random matrix ensembles”, Journal of Statistical Physics, 2013, Volume 152, Issue 1, Pages 1

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Journal of Statistical Physics, 2013, Volume 152, Issue 1, Pages 1–14
DOI: https://doi.org/10.1007/s10955-013-0761-5 (Mi jsph2)

This article is cited in 3 scientific papers (total in 3 papers)

Entropy and the Shannon–McMillan–Breiman theorem for beta random matrix ensembles

A. Bufetov^abcdef, S. Mkrtchyan^g, M. Shcherbina^h, A. Soshnikovⁱ

^a Rice University, Houston, USA
^b The Independent University of Moscow, Moscow, Russia
^c Laboratoire d'Analyse, Topologie, Probabilités, CNRS, Marseille, France
^d The Institute for Information Transmission Problems, Moscow, Russia
^e National Research University Higher School of Economics, Moscow, Russia
^f The Steklov Institute of Mathematics, Moscow, Russia
^g Carnegie Mellon University, Pittsburgh, USA
^h Institute for Low Temperature Physics Ukr. Ac. Sci., Kharkov, Ukraine
ⁱ University of California at Davis, Davis, USA

Citations (3)

DOI: https://doi.org/10.1007/s10955-013-0761-5

Abstract: We show that beta ensembles in Random Matrix Theory with generic real analytic potential have the asymptotic equipartition property. In addition, we prove a Central Limit Theorem for the density of the eigenvalues of these ensembles.

Funding agency	Grant number
Alfred P. Sloan Foundation
Dynasty Foundation
Simons Foundation
Ministry of Education and Science of the Russian Federation	MK-6734.2012.1
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Russian Foundation for Basic Research	10-01-93115-NTsNIL 11-01-00654
National Science Foundation	DMS-1007558
A. Bufetov has been supported in part by an Alfred P. Sloan Research Fellowship, a Dynasty Foundation Fellowship, as well as an IUM-Simons Fellowship, by the Grant MK-6734.2012.1 of the President of the Russian Federation, by the Programme “Dynamical systems and mathematical control theory” of the Presidium of the Russian Academy of Sciences, by the RFBR-CNRS grant 10-01-93115-NTsNIL and by the RFBR grant 11-01-00654. M. Shcherbina has been supported in part by the project “Ukrainian branch of the French-Russian Poncelet laboratory”—“Probability problems on groups and spectral theory”. A. Soshnikov has been supported in part by the NSF grant DMS-1007558.

Received: 02.01.2013
Accepted: 24.04.2013

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Document Type: Article

Language: English

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https://www.mathnet.ru/eng/jsph2

This publication is cited in the following 3 articles:

Zhiyan Shi, Xinyue Xi, Qingpei Zang, “The generalized entropy ergodic theorem for Markov chains indexed by a spherically symmetric tree”, Communications in Statistics - Theory and Methods, 53:6 (2024), 2178
Xianjie Gao, Mingliang Zhang, Jinming Luo, “Optimized Tail Bounds for Random Matrix Series”, Entropy, 26:8 (2024), 633
M. Dal Borgo, E. Hovhannisyan, A. Rouault, “Asymptotic Properties of the Density of Particles in $\beta $ β -Ensembles”, J Stat Phys, 170:3 (2018), 439

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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