Dynamics of the spherical Sherrington–Kirkpatrick model, Part II: Mixing profiles and critical dynamics
We study the Langevin dynamics of the spherical Sherrington–Kirkpatrick model, the diffusion on the sphere of radius $\sqrt N$ in $\mathbb R^N$ that is reversible with respect to the Gibbs measure with density proportional to $\exp(\beta x^{\mathsf T}Wx/\sqrt2)$, where $W$ is an $N\times N$ matrix from the Gaussian orthogonal ensemble. The dynamics is started from the uniform distribution on the sphere, independently of $W$. We determine the asymptotic quenched total-variation distance to equilibrium as a function of time in the fixed-temperature, mesoscopic, critical-window, and…
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