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arXiv · 2605.29035

The sharp log Sobolev inequality on finite cycles

Rupert L. Frank·Paata Ivanisvili
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Abstract

We settle the problem of finding the sharp constant in the log Sobolev inequality on the $n$-cycle for all $n\ge 4$, by showing that it is equal to half of the spectral gap. We deduce this result from an optimal cubic Sobolev inequality.

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Rupert L. Frank, Paata Ivanisvili. 2026-05-27. The sharp log Sobolev inequality on finite cycles. https://arxiv.org/abs/2605.29035

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