English

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 nn-cycle for all n4n\ge 4, 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

R2 v1 2026-07-22T07:38:08.979Z