FREE ENTROPY
From MaRDI portal
Publication:3152359
DOI10.1112/S0024609301008992zbMath1036.46051arXivmath/0103168MaRDI QIDQ3152359
Publication date: 22 October 2002
Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0103168
Free probability and free operator algebras (46L54) Random operators and equations (aspects of stochastic analysis) (60H25) Research exposition (monographs, survey articles) pertaining to functional analysis (46-02) Random linear operators (47B80) Measures of information, entropy (94A17)
Related Items
Large deviations for the largest eigenvalues and eigenvectors of spiked Gaussian random matrices ⋮ On the structure of non-commutative white noises ⋮ A remark on orbital free entropy ⋮ THE FREE ENTROPY DIMENSION OF SOME L∞[0,1-CIRCULAR OPERATORS] ⋮ Absence of algebraic relations and of zero divisors under the assumption of full non-microstates free entropy dimension ⋮ The free logarithmic Sobolev and the free transportation cost inequalities by time integrations ⋮ ABOUT THE QWEP CONJECTURE ⋮ A free analogue of Shannon's problem on monotonicity of entropy ⋮ An elementary approach to free entropy theory for convex potentials ⋮ Tracial smooth functions of non-commuting variables and the free Wasserstein manifold ⋮ Amenability, tubularity, and embeddings into \(\mathcal{R}^{\omega}\) ⋮ Asymptotics of rectangular spherical integrals ⋮ Hölder continuity of cumulative distribution functions for noncommutative polynomials under finite free Fisher information ⋮ \(\mathrm{MIP}^* = \mathrm{RE}\): a negative resolution to Connes' embedding problem and Tsirelson's problem ⋮ Rare events in random matrix theory ⋮ Circular law theorem for random Markov matrices ⋮ A characterization of generalized multinomial coefficients related to the entropic chain rule ⋮ REMARKS ON A SEMICIRCULAR PERTURBATION OF THE FREE FISHER INFORMATION ⋮ The Dyson equation with linear self-energy: spectral bands, edges and cusps ⋮ The Connes embedding property for quantum group von Neumann algebras ⋮ The Bi-free Extension of Free Probability ⋮ Free monotone transport ⋮ Shannon's monotonicity problem for free and classical entropy ⋮ Liberation of projections ⋮ A free stochastic partial differential equation ⋮ Orthogonal free quantum group factors are strongly 1-bounded ⋮ Free transport-entropy inequalities for non-convex potentials and application to concentration for random matrices ⋮ Loop models, random matrices and planar algebras ⋮ Orbital free pressure and its Legendre transform ⋮ A note about proving non-\(\Gamma \) under a finite non-microstates free Fisher information assumption ⋮ Topological dynamical systems associated to \(\text{II}_{1}\)-factors ⋮ Free Stein kernels and an improvement of the free logarithmic Sobolev inequality ⋮ Synchronous correlation matrices and Connes’ embedding conjecture ⋮ Remarks on free mutual information and orbital free entropy ⋮ Local limit theorems in free probability theory ⋮ Any generating set of an arbitrary property \(T\) von Neumann algebra has free entropy dimension \(\leq1\) ⋮ From Boltzmann to random matrices and beyond ⋮ ORBITAL APPROACH TO MICROSTATE FREE ENTROPY ⋮ Topological generation and matrix models for quantum reflection groups ⋮ Maximal correlation and monotonicity of free entropy and of Stein discrepancy ⋮ FREE TRANSPORTATION COST INEQUALITIES FOR NONCOMMUTATIVE MULTI-VARIABLES ⋮ Aspects of free analysis ⋮ HNN extensions of von Neumann algebras ⋮ Remarks on a free analogue of the beta prime distribution ⋮ Matrix Liberation Process II: Relation to Orbital Free Entropy ⋮ Free moment measures and laws ⋮ The Connes embedding problem: A guided tour