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J. Stat. Phys., 2013, Volume 152, Issue 1, Pages 1–14 (Mi jsph2)  

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

A. Bufetovabcdef, S. Mkrtchyang, M. Shcherbinah, 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

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.


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


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Received: 02.01.2013
Accepted:24.04.2013
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