J. Stat. Phys., 2013, Volume 152, Issue 1, Pages 1–14
(Mi jsph2)
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3 papers
Entropy and the Shannon–McMillan–Breiman theorem for beta random matrix ensembles A. Bufetov abcdef ,
S. Mkrtchyan g ,
M. Shcherbina h ,
A. Soshnikov i 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.
Received: 02.01.2013
Accepted: 24.04.2013
Language: English
DOI:
10.1007/s10955-013-0761-5
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