An elementary proof is provided of sharp bounds for the varentropy of random vectors with
log-concave densities, as well as for deviations of the information content from its mean …

For any convex body K⊆ ℝ n, S. Bubeck and R. Eldan introduced the entropic barrier on K
and showed that it is a (1+ o (1)) n-self-concordant barrier. In this note, we observe that the …

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We prove new Lipschitz properties for transport maps along heat flows, constructed by Kim
and Milman. For (semi)-log-concave measures and Gaussian mixtures, our bounds have …

We review some simple techniques based on monotone-mass transport that allow us to
obtain transport-type inequalities for any log-concave probability measures, and for more …

A special formulation of the Schrödinger problem consists in minimizing some action on the
Wasserstein space of probability measures on a Riemannian manifold subject to fixed initial …

A fundamental tool in mathematical physics is the logarithmic Sobolev inequality. A
quantitative version proven by Carlen with a remainder involving the Fourier–Wiener …

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 must be …

We investigate contraction of the Wasserstein distances on ℝ d R^d under Gaussian
smoothing. It is well known that the heat semigroup is exponentially contractive with respect …

We establish sharp exponential deviation estimates of the information content as well as a
sharp bound on the varentropy for the class of convex measures on Euclidean spaces. This …