Lower and Upper Bounds for Glauber Dynamics from Typical States of the Low-Temperature Sherrington–Kirkpatrick Model
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…
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