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Phase transition in optimal hypercontractivity
Abstract
We discover an exponent-dependent phase transition phenomenon for optimal hypercontractivity: for every prescribed q0>2, there exists a reversible continuous-time Markov chain on three state space with normalized spectral gap whose (2,q)-optimal hypercontractivity time satisfies $topt(2,q)=1/2log(q−1)$ if and only if $q≥ q0$, whereas the strict inequality topt(2,q)>1/2log(q−1) holds for 2<q<q0.
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BibTeX
@misc{cao2026phase,
title = {{Phase transition in optimal hypercontractivity}},
author = {Jie Cao and Shilei Fan and Yong Han and Yanqi Qiu and Zipeng Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15553},
eprint = {2609.15553},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15553},
}
RIS
TY - UNPB
TI - Phase transition in optimal hypercontractivity
AU - Jie Cao
AU - Shilei Fan
AU - Yong Han
AU - Yanqi Qiu
AU - Zipeng Wang
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15553
UR - https://arxiv.org/abs/2609.15553
AB - We discover an exponent-dependent phase transition phenomenon for optimal hypercontractivity: for every prescribed q_0>2, there exists a reversible continuous-time Markov chain on three state space with normalized spectral gap whose (2,q)-optimal hypercontractivity time satisfies $t_opt(2,q)=1/2log(q−1)$ if and only if $q≥ q_0$, whereas the strict inequality t_opt(2,q)>1/2log(q−1) holds for 2<q<q_0.
ER -