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Entropy and the Shannon-McMillan-Breiman theorem for beta random matrix ensembles. (English) Zbl 1283.60012
Summary: We show that beta ensembles in the 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.

60B20 Random matrices (probabilistic aspects)
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