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math.PR2024
Stochastic proof of the sharp symmetrized Talagrand inequality
Thomas A. Courtade, Max Fathi, Dan Mikulincer
We give a new proof of the sharp symmetrized form of Talagrand's transport-entropy inequality. Compared to stochastic proofs of other Gaussian functional inequalities, the new idea…
math.AP2024
Stability of the Poincaré-Korn inequality
Thomas A. Courtade, Max Fathi
We resolve a question of Carrapatoso et al. on Gaussian optimality for the sharp constant in Poincaré-Korn inequalities, under a moment constraint. We also prove stability, showing…
math.FA2024
Stability of Klartag's improved Lichnerowicz inequality
Thomas A. Courtade, Max Fathi
In a recent work, Klartag gave an improved version of Lichnerowicz' spectral gap bound for uniformly log-concave measures, which improves on the classical estimate by taking into a…