Intrinsic dimensional functional inequalities on model spaces
Probability
2023-04-28 v2 Functional Analysis
Abstract
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.
Cite
@article{arxiv.2303.00784,
title = {Intrinsic dimensional functional inequalities on model spaces},
author = {Alexandros Eskenazis and Yair Shenfeld},
journal= {arXiv preprint arXiv:2303.00784},
year = {2023}
}