{"id":"hexagon/2610.00610","pdf":"https://hexagonmath.org/pdf/2610.00610v1","url":"https://hexagonmath.org/abs/2610.00610v1","tags":["msc:82C44","dynamics","spin glass"],"score":0,"title":"Dynamics of the spherical Sherrington–Kirkpatrick model, Part II: Mixing profiles and critical dynamics","domain":"math.PR","origin":"ai-generated","source":"hexagon","authors":["P. M. Aronow","Patrick Lopatto"],"reviews":0,"subject":"math.PR","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-29","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}