The sharp log Sobolev inequality on finite cycles
Analysis of PDEs
2026-05-29 v1 Classical Analysis and ODEs
Functional Analysis
Abstract
We settle the problem of finding the sharp constant in the log Sobolev inequality on the -cycle for all , by showing that it is equal to half of the spectral gap. We deduce this result from an optimal cubic Sobolev inequality.
Keywords
Cite
@article{arxiv.2605.29035,
title = {The sharp log Sobolev inequality on finite cycles},
author = {Rupert L. Frank and Paata Ivanisvili},
journal= {arXiv preprint arXiv:2605.29035},
year = {2026}
}
Comments
16 pages