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Displaying similar documents to “A large deviation theorem for the empirical eigenvalue distribution of random unitary matrices”

A log-Sobolev type inequality for free entropy of two projections

Fumio Hiai, Yoshimichi Ueda (2009)

Annales de l'I.H.P. Probabilités et statistiques

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We prove a kind of logarithmic Sobolev inequality claiming that the mutual free Fisher information dominates the microstate free entropy adapted to projections in the case of two projections.

Convex entropy decay via the Bochner–Bakry–Emery approach

Pietro Caputo, Paolo Dai Pra, Gustavo Posta (2009)

Annales de l'I.H.P. Probabilités et statistiques

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We develop a method, based on a Bochner-type identity, to obtain estimates on the exponential rate of decay of the relative entropy from equilibrium of Markov processes in discrete settings. When this method applies the relative entropy decays in a convex way. The method is shown to be rather powerful when applied to a class of birth and death processes. We then consider other examples, including inhomogeneous zero-range processes and Bernoulli–Laplace models. For these two models, known...

Voiculescu’s Entropy and Potential Theory

Thomas Bloom (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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We give a new proof, relying on polynomial inequalities and some aspects of potential theory, of large deviation results for ensembles of random hermitian matrices.

Entropy of random walk range

Itai Benjamini, Gady Kozma, Ariel Yadin, Amir Yehudayoff (2010)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

We study the entropy of the set traced by an -step simple symmetric random walk on ℤ. We show that for ≥3, the entropy is of order . For =2, the entropy is of order /log2. These values are essentially governed by the size of the boundary of the trace.