61 citations · 174 across the 27 of their papers we have counts for
31 papers
Transportation onto log-Lipschitz perturbations
Max Fathi, Dan Mikulincer, Yair Shenfeld
We establish sufficient conditions for the existence of globally Lipschitz transport maps between probability measures and their log-Lipschitz perturbations, with dimension-free bo…
Stability estimates for the sharp spectral gap bound under a curvature-dimension condition
Max Fathi, Ivan Gentil, Jordan Serres
We study stability of the sharp spectral gap bounds for metric-measure spaces satisfying a curvature bound. Our main result, new even in the smooth setting, is a sharp quantitative…
Bounds in Wasserstein distance on the normal approximation of general M-estimators
François Bachoc, Max Fathi
We derive quantitative bounds on the rate of convergence in Wasserstein distance of general M-estimators, with an almost sharp (up to a logarithmic term) behavior in the numb…
Stability of eigenvalues and observable diameter in RCD spaces
Jérôme Bertrand, Max Fathi
We study stability of the spectral gap and observable diameter for metricmeasure spaces satisfying the RCD(1, ) condition. We show that if such a space has an almost maxima…
Stability estimates for invariant measures of diffusion processes, with applications to stability of moment measures and Stein kernels
Max Fathi, Dan Mikulincer
We investigate stability of invariant measures of diffusion processes with respect to distances on the coefficients, under an assumption of log-concavity. The method is a var…
Relaxing the Gaussian assumption in Shrinkage and SURE in high dimension
Max Fathi, Larry Goldstein, Gesine Reinert +1
Shrinkage estimation is a fundamental tool of modern statistics, pioneered by Charles Stein upon his discovery of the famous paradox involving the multivariate Gaussian. A large po…
Self-improvement of the Bakry-Emery criterion for Poincar{é} inequalities and Wasserstein contraction using variable curvature bounds
Patrick Cattiaux, Max Fathi, Arnaud Guillin
We study Poincar{é} inequalities and long-time behavior for diffusion processes on R^n under a variable curvature lower bound, in the sense of Bakry-Emery. We derive various estima…
Bounds on optimal transport maps onto log-concave measures
Maria Colombo, Max Fathi
We consider strictly log-concave measures, whose bounds degenerate at infinity. We prove that the optimal transport map from the Gaussian onto such a measure is locally Lipschitz,…
Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces
Matthias Erbar, Max Fathi, André Schlichting
We consider non-linear evolution equations arising from mean-field limits of particle systems on discrete spaces. We investigate a notion of curvature bounds for these dynamics bas…
A proof of the Caffarelli contraction theorem via entropic regularization
Max Fathi, Nathael Gozlan, Maxime Prodhomme
We give a new proof of the Caffarelli contraction theorem, which states that the Brenier optimal transport map sending the standard Gaussian measure onto a uniformly log-concave pr…
Higher-order Stein kernels for Gaussian approximation
Max Fathi
We introduce higher-order Stein kernels relative to the standard Gaussian measure, which generalize the usual Stein kernels by involving higher-order derivatives of test functions.…
A note on existence of free Stein kernels
Guillaume Cébron, Max Fathi, Tobias Mai
Stein kernels are a way of comparing probability distributions, defined via integration by parts formulas. We provide two constructions of Stein kernels in free probability. One is…
Stability of the Bakry-Emery theorem on
Thomas A. Courtade, Max Fathi
We prove stability estimates for the Bakry-Emery bound on Poincaré and logarithmic Sobolev constants of uniformly log-concave measures. In particular, we improve the quantitative b…
A sharp symmetrized form of Talagrand's transport-entropy inequality for the Gaussian measure
Max Fathi
This note presents a sharp transport-entropy inequality that improves on Talagrand's inequality for the Gaussian measure, arising as a dual formulation of the functional Santaló in…
Stein kernels and moment maps
Max Fathi
We describe a construction of Stein kernels using moment maps, which are solutions to a variant of the Monge-Ampère equation. As a consequence, we show how regularity bounds on the…
Existence of Stein Kernels under a Spectral Gap, and Discrepancy Bound
Thomas A. Courtade, Max Fathi, Ashwin Pananjady
We establish existence of Stein kernels for probability measures on satisfying a Poincaré inequality, and obtain bounds on the Stein discrepancy of such measures. Ap…
Poincaré, modified logarithmic Sobolev and isoperimetric inequalities for Markov chains with non-negative Ricci curvature
Matthias Erbar, Max Fathi
We study functional inequalities for Markov chains on discrete spaces with entropic Ricci curvature bounded from below. Our main results are that when curvature is non-negative, bu…
Wasserstein Stability of the Entropy Power Inequality for Log-Concave Densities
Thomas A. Courtade, Max Fathi, Ashwin Pananjady
We establish quantitative stability results for the entropy power inequality (EPI). Specifically, we show that if uniformly log-concave densities nearly saturate the EPI, then they…
Free Stein kernels and an improvement of the free logarithmic Sobolev inequality
Max Fathi, Brent Nelson
We introduce a free version of the Stein kernel, relative to a semicircular law. We use it to obtain a free counterpart of the HSI inequality of Ledoux, Peccatti and Nourdin, which…
Gradient flow structure for McKean-Vlasov equations on discrete spaces
Matthias Erbar, Max Fathi, Vaios Laschos +1
In this work, we show that a family of non-linear mean-field equations on discrete spaces can be viewed as a gradient flow of a natural free energy functional with respect to a cer…
Curvature and transport inequalities for Markov chains in discrete spaces
Max Fathi, Yan Shu
We study various transport-information inequalities under three different notions of Ricci curvature in the discrete setting: the curvature-dimension condition of Bakry and Émery,…
The gradient flow approach to hydrodynamic limits for the simple exclusion process
Max Fathi, Marielle Simon
We give a new approach to the well-known convergence to the hydrodynamic limit for the symmetric simple exclusion process (SSEP). More precisely, we characterize any possible limit…
Entropic Ricci curvature bounds for discrete interacting systems
Max Fathi, Jan Maas
We develop a new and systematic method for proving entropic Ricci curvature lower bounds for Markov chains on discrete sets. Using different methods, such bounds have recently been…
Quantitative logarithmic Sobolev inequalities and stability estimates
Max Fathi, Emanuel Indrei, Michel Ledoux
We establish an improved form of the classical logarithmic Sobolev inequality for the Gaussian measure restricted to probability densities which satisfy a Poincaré inequality. The…