Logarithmic Sobolev Inequalities
1975/01/01 by Leonard Gross · 97 citations
Mathematics · Decision Sciences · #Nonlinear Partial Differential Equations #Probabilistic and Robust Engineering Design #Mathematical Approximation and Integration
paper · doi:10.2307/2373688
Cited by
- The sharp log Sobolev inequality on finite cycles
- Almost monotonicity formulas for elliptic and parabolic operators with variable coefficients
- One-dimensional Gagliardo-Nirenberg-Sobolev inequalities: remarks on duality and flows
- Bounds on the deficit in the logarithmic Sobolev inequality
- Solution of a class of reaction-diffusion systems via logarithmic Sobolev inequality
- Chaos, concentration, and multiple valleys
- Convex Sobolev inequalities and spectral gap
- A parabolic problem involving p(x)-Laplacian, a power and a singular nonlinearity
- Intrinsic Ultracontractivity on Riemannian Manifolds with Infinite Volume Measures
- Ergodicity of scalar stochastic differential equations with H "older\n continuous coefficients
- Four Talagrand inequalities under the same umbrella
- Sharp reversed Hardy-Littlewood-Sobolev inequality with extended kernel
- Some inequalities on Riemannian manifolds linking Entropy,Fisher information, Stein discrepancy and Wasserstein distance
- Analysis on Wiener Space and Applications
- Hydrodynamic limit for conservative spin systems with super-quadratic,\n partially inhomogeneous single-site potential
- Asymptotics of spectral gaps on loop spaces over a class of Riemannian manifolds
- Symmetric Ornstein-Uhlenbeck Semigroups and their Generators
- Sharp Hardy-Littlewood-Sobolev inequality on the upper half space
- Polyharmonic Nonlinear Scalar Field Equations
- Generalization error of random features and kernel methods: hypercontractivity and kernel matrix concentration
- Logarithmic Sobolev-type inequalities on Lie groups
- Minimal hypersurfaces and geometric inequalities
- The nonlinear porous medium equation for the f-Laplacian: Hamilton-Souplet-Zhang type gradient estimates and implications
- Stability in Gagliardo-Nirenberg-Sobolev inequalities: flows, regularity and the entropy method
- Remarks on a free analogue of the beta prime distribution
- Covariance-Modulated Optimal Transport and Gradient Flows
- Lipschitz continuity of solutions of Poisson equations in metric measure spaces
- On extracting common random bits from correlated sources on large alphabets
- Chemotaxis and Reactions in Biology
- An Asymmetric Affine Pólya--Szegö Principle
- Learning with invariances in random features and kernel models
- On the Convergence of Langevin Monte Carlo: The Interplay between Tail Growth and Smoothness
- A regularity lemma, and low-weight approximators, for low-degree polynomial threshold functions
- Links between the Logarithmic Sobolev Inequality and the convolution\n inequalities for Entropy and Fisher Information
- Logarithmic Sobolev Trace Inequalities
- Logarithmic Sobolev inequalities for finite Markov chains
- On reverse hypercontractivity
- Regularization in L1 for the Ornstein--Uhlenbeck semigroup
- Monotonicity - analytic and geometric implications
- Information-Theoretic Inequalities on Unimodular Lie Groups
- Global existence and blow-up of solutions to a class of non-Newton filtration equations with singular potential and logarithmic nonlinearity
- The log-Sobolev inequality for the ground state of a Schrödinger operator on bounded convex domains
- Limit Theorems in Warsserstein Distance for Empirical Measures of Diffusion Processes on Riemannian Manifolds
- An Efficient Sampling Algorithm for Non-smooth Composite Potentials
- Integrated Harnack inequalities on Lie groups
- The East model: recent results and new progresses
- Deficit Estimates for the Logarithmic Sobolev Inequality
- Lq-functional inequalities and weighted porous media equations
- On a class of stochastic semilinear PDE's
- Geometric Approach Towards Complete Logarithmic Sobolev Inequalities
- Generalised Brownian bridges: examples
- Improved Approximation of Linear Threshold Functions
- Entropy and heat kernel bounds on a Ricci flow background
- Entropy dissipation via Information Gamma calculus: Non-reversible stochastic differential equations
- Time memory effect in entropy decay of Ornstein-Uhlenbeck operators
- Poincaré type inequalities for group measure spaces and related transportation cost inequalities
- Criteria of Spectral Gap for Markov Operators
- Regularisation effects of nonlinear semigroups
- Characterizations of Bounded Ricci Curvature on Smooth and NonSmooth Spaces
- Hypercontractivity in Non-Commutative Holomorphic Spaces
- Propagation of Localization Optimal Entropy Production and Convergence rates for the Central Limit Theorem
- Deficit functions and the log Sobolev inequality
- Hierarchic flows to estimate and sample high-dimensional probabilities
- Sufficient Conditions for the Invertibility of Adapted Perturbations of Identity on the Wiener Space
- An extension of the Beckner's type Poincar 'e inequality to convolution\n measures on abstract Wiener spaces
- Generalization error of random feature and kernel methods: Hypercontractivity and kernel matrix concentration
- Entropy Jumps for Radially Symmetric Random Vectors
- Learning with convolution and pooling operations in kernel methods
- Lectures on noise sensitivity and percolation
- Super and Weak Poincaré Inequalities for Sticky-Reflected Diffusion Processes
- Biharmonic nonlinear vector field equations in ℝ4
- Functional Inequalities for Stable-Like Dirichlet Forms
- Sharp Logarithmic Sobolev and related inequalities with monomial weights
- Improved Hölder and reverse Hölder inequalities for correlated Gaussian random vectors
- Hypercontractivity and asymptotic behaviour in nonautonomous Kolmogorov equations
- On the Bakry-Emery criterion for linear diffusions and weighted porous media equations
- Causal transference plans and their Monge-Kantorovich problems
- A probabilistic framework for approximating functions in active subspaces
- The deficit in the Gaussian log-Sobolev inequality and inverse Santalo inequalities
- Isoperimetric estimates for the first Neumann eigenvalue of Hermite differential equations
- The local entropy along Ricci flow---Part A: the no-local-collapsing theorems
- Analysis of a one-dimensional forager-exploiter model
- On the Semi-Classical Brownian Bridge Measure
- Capacity Upper Bounds for the Relay Channel via Reverse Hypercontractivity
- A modified logarithmic Sobolev inequality for the Hamming cube and some applications
- Two limits on Hardy and Sobolev inequalities
- Coarsen entropy inequalities and its applications in quantitative stochastic homogenization
- The logarithmic Sobolev inequality for a submanifold in Euclidean space
- Characterizations of matrix and operator-valued Φ-entropies, and operator Efron-Stein inequalities. [europepmc]
- A family of wave equations with some remarkable properties. [europepmc]
- Ornstein-Uhlenbeck semigroups in infinite dimension. [europepmc]
- The Ornstein-Uhlenbeck semigroup in finite dimension. [europepmc]
- A Forward-Reverse Brascamp-Lieb Inequality: Entropic Duality and Gaussian Optimality. [europepmc]
- Hypercontractive Inequalities for the Second Norm of Highly Concentrated Functions, and Mrs. Gerber's-Type Inequalities for the Second Rényi Entropy. [europepmc]
- An Information-Theoretic Proof of a Hypercontractive Inequality. [europepmc]
- Weighted Aronson-Bénilan estimates and Harnack inequalities for slow diffusion equations with a nonlinear forcing term. [europepmc]
- The nonlinear porous medium equation for the f -Laplacian: Hamilton-Souplet-Zhang type gradient estimates and implications. [europepmc]