Tracial smooth functions of non-commuting variables and the free Wasserstein manifold
From MaRDI portal
Publication:5089672
DOI10.4064/dm843-10-2021zbMath1502.46052arXiv2101.06572OpenAlexW3124898035MaRDI QIDQ5089672
Dimitri Shlyakhtenko, David Jekel, Wuchen Li
Publication date: 20 July 2022
Published in: Dissertationes Mathematicae (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2101.06572
Free probability and free operator algebras (46L54) Measures of information, entropy (94A17) Noncommutative function spaces (46L52) Spaces and manifolds of mappings (including nonlinear versions of 46Exx) (58D99) Transport equations (35Q49)
Related Items (5)
\(\mathrm{C}^\ast\)-algebras. Abstracts from the workshop held August 7--13, 2022 ⋮ Invariant structure preserving functions and an Oka-Weil Kaplansky density type theorem ⋮ Vanishing first cohomology and strong 1-boundedness for von Neumann algebras ⋮ Computing the spectral action for fuzzy geometries: from random noncommutative geometry to bi-tracial multimatrix models ⋮ Duality for optimal couplings in free probability
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Functions of noncommuting self-adjoint operators under perturbation and estimates of triple operator integrals
- An analog of the 2-Wasserstein metric in non-commutative probability under which the fermionic Fokker-Planck equation is gradient flow for the entropy
- Free monotone transport
- Model theory of operator algebras. II: Model theory
- Free probability and random matrices
- Free diffusions and matrix models with strictly convex interaction
- Lower estimates on microstates free entropy dimension
- Operator Hölder-Zygmund functions
- Addition of certain non-commuting random variables
- A new example of `independence' and `white noise'
- The analogues of entropy and of Fisher's information measure in free probability theory. V: Noncommutative Hilbert transforms
- Limit laws for random matrices and free products
- A heat semigroup approach to concentration on the sphere and on a compact Riemannian manifold
- The invariant theory of \(n\times n\) matrices
- On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
- Trace identities and polynomial identities of \(n\times n\) matrices
- Stochastic calculus with respect to free Brownian motion and analysis on Wigner space
- The analogues of entropy and of Fisher's information measure in free probability theory. I
- The analogues of entropy and of Fisher's information measure in free probability theory. II
- Combinatorial properties of Brownian motion on the compact classical groups
- Large deviation bounds for matrix Brownian motion
- Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
- Concentration of the spectral measure for large matrices
- On the statistical mechanics approach in the random matrix theory: Integrated density of states.
- From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalities
- A discrete Schrödinger equation via optimal transport on graphs
- The analogues of entropy and of Fisher's information measure in free probability theory. VI: Liberation and mutual free information
- Free Fisher information for non-tracial states.
- Free transportation cost inequalities via random matrix approximation
- Asymptotic expansion of \(\beta \) matrix models in the one-cut regime
- Maximal correlation and monotonicity of free entropy and of Stein discrepancy
- Transport information geometry: Riemannian calculus on probability simplex
- A hydrodynamic exercise in free probability: setting up free Euler equations
- Free transport-entropy inequalities for non-convex potentials and application to concentration for random matrices
- Free monotone transport without a trace
- Algorithm for Hamilton-Jacobi equations in density space via a generalized Hopf formula
- Free transport for finite depth subfactor planar algebras
- Heat kernel empirical laws on \({\mathrm {U}}_N\) and \({\mathrm {GL}}_N\)
- The large-\(N\) limit of the Segal-Bargmann transform on \(\mathbb U_N\)
- Free convolution operators and free Hall transform
- Multiple operator integrals and higher operator derivatives
- Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits
- Groups of diffeomorphisms and the motion of an incompressible fluid
- Free analog of pressure and its Legendre transform
- Determinant theory in finite factors
- An elementary approach to free entropy theory for convex potentials
- On the law of large numbers for the empirical measure process of generalized Dyson Brownian motion
- THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
- On Matrix-Valued Monge–Kantorovich Optimal Mass Transport
- Functions of perturbed unbounded self-adjoint operators. Operator Bernstein type inequalities
- Free Random Variables
- FREE ENTROPY
- Free transport for convex potentials
- Lectures on the Combinatorics of Free Probability
- Large-NAsymptotic Expansion for Mean Field Models with Coulomb Gas Interaction
- TRACE IDENTITIES AND CENTRAL POLYNOMIALS IN THE MATRIX SUPERALGEBRAS $ M_{n,k}$
- The Density Manifold and Configuration Space Quantization
- TRACE IDENTITIES OF FULL MATRIX ALGEBRAS OVER A FIELD OF CHARACTERISTIC ZERO
- Logarithmic Sobolev Inequalities
- The Variational Formulation of the Fokker--Planck Equation
- There is no separable universal 𝐼𝐼₁-factor
- The Large-NLimits of Brownian Motions on 𝔾𝕃N
- Matrix Optimal Mass Transport: A Quantum Mechanical Approach
- Conditional Expectation, Entropy, and Transport for Convex Gibbs Laws in Free Probability
- On Optimal Transport of Matrix-Valued Measures
- Multiple operator integrals, Haagerup and Haagerup‐like tensor products, and operator ideals
- FREE TRANSPORTATION COST INEQUALITIES FOR NONCOMMUTATIVE MULTI-VARIABLES
- Triangular transformations of measures
- Formes linéaires sur un anneau d'opérateurs
- Hessian metric via transport information geometry
- Optimal Transport
- Free diffusions, free entropy and free Fisher information
- A free probability analogue of the Wasserstein metric on the trace-state space
This page was built for publication: Tracial smooth functions of non-commuting variables and the free Wasserstein manifold
