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- W2341016751 abstract "We prove that the $limsup$ and $liminf$ variants of Voiculescu's free entropy coincide. This is based on a Laplace principle (implying a full large deviation principle) for hermitian brownian motion on $[0,1]$. As a consequence, we show that microstates free entropy $chi(X_1,...,X_m)$ and non-microstate free entropy $chi^*(X_1,...,X_m)$ coincide for self-adjoint variables $(X_1,...,X_m)$ satisfying a Schwinger-Dyson equation for subquadratic, bounded bellow, strictly convex potentials with Lipschitz derivative sufficiently approximable by non-commutative polynomials. Applying the contraction principle, we obtain a large deviation result for Haar unitaries and deduce the most general additivity property for a new extended definition of orbital free entropy. Our results are based on Dupuis-Ellis weak convergence approach to large deviations, where one shows a Laplace principle in obtaining a stochastic control formulation for exponential functionals. In the non-commutative context, ultrapoduct analysis replaces weak-convergence of the stochastic control problems." @default.
- W2341016751 created "2016-06-24" @default.
- W2341016751 creator A5052788604 @default.
- W2341016751 date "2016-04-21" @default.
- W2341016751 modified "2023-09-27" @default.
- W2341016751 title "A Laplace Principle for Hermitian Brownian Motion and Free Entropy" @default.
- W2341016751 hasPublicationYear "2016" @default.
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