Manual The semicircle law, free random variables and entropy

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Ercolani, N.

The Semicircle Law, Free Random Variables and Entropy

Asymptotics of the partition function for random matrices via Riemann-Hilbert techniques and applications to graphical enumeration. Correlation functions of Harish-Chandra integrals over the orthogonal and the symplectic groups - Ferrer, A. Prats et al. First order asymptotics of matrix integrals.

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Combinatorial aspects of matrix models. Second order asymptotics for matrix models. Annals Probab.

Large deviations asymptotics for spherical integrals. Hiai, F..

The Semicircle Law, Free Random Variables and Entropy

Surveys Monogr. High order expansion for matrix models and enumeration of maps.

Next, the perturbation theory for compactly supported probability measures via free relative entropy is developed on the analogy of the perturbation theory via relative entropy. When the perturbed measure via relative entropy is suitably arranged on the space of selfadjoint matrices and the matrix size goes to infinity, it is proven that the perturbation via relative entropy on the matrix space approaches asymptotically to that via free relative entropy. The whole theory can be adapted to probability measures on the unit circle. Source J. Japan , Volume 54, Number 3 , Zentralblatt MATH identifier Share full text access.


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The Semicircle Law, Free Random Variables and Entropy Mathematical Surveys and Monographs

Purchase Instant Access. View Preview. Learn more Check out. Abstract Free entropy is the analogue of entropy in free probability theory. Citing Literature. Volume 34 , Issue 3 May Pages Related Information.