Ergodicity of infinite volume $Φ^4_3$ at high temperature

Fuente: arXiv
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Main Authors: Duch, Paweł, Hairer, Martin, Yi, Jaeyun, Zhao, Wenhao
Format: Preprint
Published: 2025
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author Duch, Paweł
Hairer, Martin
Yi, Jaeyun
Zhao, Wenhao
author_facet Duch, Paweł
Hairer, Martin
Yi, Jaeyun
Zhao, Wenhao
contents We consider the infinite volume $Φ^4_3$ dynamic and show that it is globally well-posed in a suitable weighted Besov space of distributions. At high temperatures / small coupling, we furthermore show that the difference between any two solutions driven by the same realisation of the noise converges to zero exponentially fast. This allows us to characterise the infinite-volume $Φ^4_3$ measure at high temperature as the unique invariant measure of the dynamic, and to prove that it satisfies all Osterwalder--Schrader axioms, including invariance under translations, rotations, and reflections, as well as exponential decay of correlations.
format Preprint
id arxiv_https___arxiv_org_abs_2508_07776
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Ergodicity of infinite volume $Φ^4_3$ at high temperature
Duch, Paweł
Hairer, Martin
Yi, Jaeyun
Zhao, Wenhao
Probability
Mathematical Physics
Analysis of PDEs
60H15, 60H17, 60L30, 81T08, 81S20
We consider the infinite volume $Φ^4_3$ dynamic and show that it is globally well-posed in a suitable weighted Besov space of distributions. At high temperatures / small coupling, we furthermore show that the difference between any two solutions driven by the same realisation of the noise converges to zero exponentially fast. This allows us to characterise the infinite-volume $Φ^4_3$ measure at high temperature as the unique invariant measure of the dynamic, and to prove that it satisfies all Osterwalder--Schrader axioms, including invariance under translations, rotations, and reflections, as well as exponential decay of correlations.
title Ergodicity of infinite volume $Φ^4_3$ at high temperature
topic Probability
Mathematical Physics
Analysis of PDEs
60H15, 60H17, 60L30, 81T08, 81S20
url https://arxiv.org/abs/2508.07776