61 citations · 174 across the 27 of their papers we have counts for
5 papers · 1 filter
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…