Yair Shenfeld

The extremals of the Alexandrov–Fenchel inequality for convex polytopes

Acta Mathematica · 2023-01-01 · 21 citations

extremals of the alexandrov-fenchel inequality 95 of the settings considered by Stanley, where N i is the number of linear extensions of a partially ordered set for which a distinguished element has rank i.Such extremal problems appear to be inaccessible by currently known methods of enumerative or algebraic combinatorics.This example highlights the significance of the questions considered in this paper to extremal problems in other areas of mathematics, and hints at the possibility that the str…

The extremals of Stanley's inequalities for partially ordered sets

Advances in Mathematics · 2023-11-24 · 8 citations

Intrinsic dimensional functional inequalities on model spaces

Journal of Functional Analysis · 2024-01-26 · 7 citations

We initiate a systematic study of intrinsic dimensional versions of classical functional inequalities which capture refined properties of the underlying objects. We focus on model spaces: Euclidean space, Hamming cube, and manifolds of constant curvature. In the latter settings, our intrinsic dimensional functional inequalities improve on a series of known results and lead to new Hamilton-type matrix inequalities. Our proofs rely on scaling, tensorization, and stochastic methods.

The Brownian transport map

Probability Theory and Related Fields · 2024-05-16 · 6 citations

Contraction properties of transport maps between probability measures play an important role in the theory of functional inequalities. The actual construction of such maps, however, is a non-trivial task and, so far, relies mostly on the theory of optimal transport. In this work, we take advantage of the infinite-dimensional nature of the Gaussian measure and construct a new transport map, based on the Föllmer process, which pushes forward the Wiener measure onto probability measures on Euclidea…

Transportation onto log-Lipschitz perturbations

Calculus of Variations and Partial Differential Equations · 2024-02-20 · 6 citations