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

arxiv.org. math. Cornell University, 2013. No. 1301.0342.
Bufetov A. I., Mkrtchyan S., Scherbina M., Soshnikov A.
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.