{"id":"hexagon/2610.00402","pdf":"https://hexagonmath.org/pdf/2610.00402v1","url":"https://hexagonmath.org/abs/2610.00402v1","tags":["math.MP","math-ph","msc:82B44"],"score":0,"title":"Lower and Upper Bounds for Glauber Dynamics from Typical States of the Low-Temperature Sherrington–Kirkpatrick Model","domain":"math.PR","origin":"ai-generated","source":"hexagon","authors":["P. M. Aronow","Patrick Lopatto"],"reviews":0,"subject":"math.PR","summary":"We study the heat-bath (Glauber) dynamics of the Sherrington–Kirkpatrick model at zero external field and fixed inverse temperature $\\beta>1$. We sample the disorder $J$ and an initial configuration $X_0$ from its Gibbs measure. Let $T^J(X_0)$ be the time at which the transition law, conditional on $J$ and the realized $X_0$, first comes within total-variation distance $1/4$ of equilibrium. In continuous time, with rate one per site, we prove that, for every fixed $\\omega\\in(0,1/4)$, with probability tending to one, \\[ A_\\beta n^{7/30} 0$ depends only on $\\beta$. Corresponding bounds hold…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-20","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}