Logarithmic bounds for isoperimetry and slices of convex sets Page 1 Ars Inveniendi Analytica
(2023), Paper No. 4, 17 pp. DOI 10.15781/jsjy-0b06 ISSN: 2769-8505 Logarithmic bounds for …

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 …

We study the isoperimetric, functional and concentration properties of $ n $-dimensional
weighted Riemannian manifolds satisfying the Curvature-Dimension condition, when the …

It is known that by dualizing the Bochner–Lichnerowicz–Weitzenböck formula, one obtains
Poincaré-type inequalities on Riemannian manifolds equipped with a density, which satisfy …

Let μ be a probability measure on R n (n≥ 2) with Lebesgue density proportional to e− V (‖
x‖), where V: R+→ R is a smooth convex potential. We show that the associated spectral …

In this work, we consider dimensional improvements of the logarithmic Sobolev, Talagrand
and Brascamp–Lieb inequalities. For this, we use optimal transport methods and the Borell …

In this paper, we offer a proof for a family of functional inequalities interpolating between the
Poincaré and the logarithmic Sobolev (standard and weighted) inequalities. The proofs rely …

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 …

Let μ be a log-concave probability measure on R n and for any N> n consider the random
polytope KN= conv {X 1,…, XN}, where X 1, X 2,… are independent random points in R n …