The analogues of entropy and of Fisher's information measure in free probability theory. II
From MaRDI portal
Publication:1340632
DOI10.1007/BF01231539zbMath0820.60001OpenAlexW2019667538MaRDI QIDQ1340632
Publication date: 31 August 1995
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/144242
logarithmic energyfree entropy dimensionfree group factorsnoncommutative functional calculusstatistical weight of approximating microstates
Related Items
Large deviations upper bounds for the laws of matrix-valued processes and non-commutative entropies, The non-microstates free entropy dimension of DT-operators, Free transportation cost inequalities via random matrix approximation, A remark on orbital free entropy, A log-Sobolev type inequality for free entropy of two projections, Free entropy dimension and regularity of non-commutative polynomials, Analytic subordination for bi-free convolution, Convergence of the empirical spectral distribution of Gaussian matrix-valued processes, COLLECTIVE POTENTIAL FOR LARGE-N HAMILTONIAN MATRIX MODELS AND FREE FISHER INFORMATION, THE FREE ENTROPY DIMENSION OF SOME L∞[0,1-CIRCULAR OPERATORS], A MICROSTATES APPROACH TO RELATIVE FREE ENTROPY, ENTROPY OF OPERATOR-VALUED RANDOM VARIABLES: A VARIATIONAL PRINCIPLE FOR LARGE N MATRIX MODELS, On the classification of full factors of type III, Absence of algebraic relations and of zero divisors under the assumption of full non-microstates free entropy dimension, Free orbit dimension of finite von Neumann algebras, Dimension and entropy computations for \(L(F_{r})\), ABOUT THE QWEP CONJECTURE, A free analogue of Shannon's problem on monotonicity of entropy, Symmetry in tensor algebras over Hilbert space, The analogues of entropy and of Fisher's information measure in free probability theory. III: The absence of Cartan subalgebras, An elementary approach to free entropy theory for convex potentials, Large deviations and linear statistics for potential theoretic ensembles associated with regular closed sets, On finite free Fisher information for eigenvectors of a modular operator, Cyclic Hilbert spaces and Connes' embedding problem, Analytic subordination theory of operator-valued free additive convolution and the solution of a general random matrix problem, Tracial smooth functions of non-commuting variables and the free Wasserstein manifold, A random matrix approach to the Peterson-Thom conjecture, COMPUTABILITY AND THE CONNES EMBEDDING PROBLEM, Asymptotics of rectangular spherical integrals, Information in Probability: Another Information-Theoretic Proof of a Finite de Finetti Theorem, Concavification of free entropy, Remarks on the diagonal embedding and strong 1-boundedness, Globally trace-positive noncommutative polynomials and the unbounded tracial moment problem, An exotic \(\mathrm{II}_1\) factor without property Gamma, Free component analysis: theory, algorithms and applications, Hölder continuity of cumulative distribution functions for noncommutative polynomials under finite free Fisher information, An inequality for non-microstates free entropy dimension for crossed products by finite abelian groups, \(\mathrm{MIP}^* = \mathrm{RE}\): a negative resolution to Connes' embedding problem and Tsirelson's problem, Convergence for noncommutative rational functions evaluated in random matrices, The free field: realization via unbounded operators and Atiyah property, Covering entropy for types in tracial W<sup>*</sup>-algebras, Freeness and matrix decompositions, A modified version of free orbit-dimension of von Neumann algebras, Vanishing first cohomology and strong 1-boundedness for von Neumann algebras, Microstates free entropy and cost of equivalence relations, Around the circular law, FREE ENTROPY DIMENSION OF PROJECTIONS AND FACTORIALITY OF GENERATED VON NEUMANN ALGEBRAS, A mass-transportation approach to a one dimensional fluid mechanics model with nonlocal velocity, REMARKS ON A SEMICIRCULAR PERTURBATION OF THE FREE FISHER INFORMATION, The Dyson equation with linear self-energy: spectral bands, edges and cusps, An alternative to free entropy for free group factors, Logarithmic Sobolev inequalities, matrix models and free entropy, The Connes embedding property for quantum group von Neumann algebras, Voiculescu's entropy and potential theory, Analogues of entropy in bi-free probability theory: non-microstate, On the supports of measures in free multiplicative convolution semigroups, Prime factors, Free monotone transport, Amalgamated free products of weakly rigid factors and calculation of their symmetry groups, Notes on microstate free entropy of projections, Free probability and the von Neumann algebras of free groups, A free stochastic partial differential equation, On some decomposition properties for factors of type \(\text{II}_1\), The Effros-Maréchal topology in the space of von Neumann algebras. II, On classical analogues of free entropy dimension, Tracial stability for \(C^*\)-algebras, Orthogonal free quantum group factors are strongly 1-bounded, Connes' embedding conjecture and sums of Hermitian squares, Strong 1-boundedness of unimodular orthogonal free quantum groups, Stability under small Hilbert-Schmidt perturbations for \(C^\ast\)-algebras, Model theory of operator algebras III: elementary equivalence and II1factors, Orbital free pressure and its Legendre transform, Atoms and regularity for measures in a partially defined free convolution semigroup, Free Stein kernels and an improvement of the free logarithmic Sobolev inequality, Free group factors and factors with some decompositions, Fractal entropies and dimensions for microstates spaces, Synchronous correlation matrices and Connes’ embedding conjecture, Unbounded derivations, free dilations, and indecomposability results for II$_1$ factors, The free entropy dimension of hyperfinite von Neumann algebras, Any generating set of an arbitrary property \(T\) von Neumann algebra has free entropy dimension \(\leq1\), Topological free entropy dimension for approximately divisible \(C^*\)-algebras, ORBITAL APPROACH TO MICROSTATE FREE ENTROPY, Topological free entropy dimension in unital \(C^*\)-algebras, Maximal correlation and monotonicity of free entropy and of Stein discrepancy, FREE TRANSPORTATION COST INEQUALITIES FOR NONCOMMUTATIVE MULTI-VARIABLES, Free analog of pressure and its Legendre transform, Random regularization of Brown spectral measure, Free subproducts and free scaled products of II\(_{1}\)-factors, \(A\)-valued semicircular systems, Duality for optimal couplings in free probability, Free moment measures and laws, Eigenvalue Density of the Wishart Matrix and Large Deviations, Discussions around Voiculescu's free entropies.
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Limit laws for random matrices and free products
- Free products of hyperfinite von Neumann algebras and free dimension
- The analogues of entropy and of Fisher's information measure in free probability theory. I
- Interpolated free group factors
- On non-semisplit extensions, tensor products and exactness of group \(C^*\)-algebras
- Free Random Variables