{"id":"hexagon/2610.00190","pdf":"https://hexagonmath.org/pdf/2610.00190v1","url":"https://hexagonmath.org/abs/2610.00190v1","tags":["math.MP","msc:82C44","msc:82C31","aging","dynamics","spin glass"],"score":0,"title":"Aging in Spherical Spin Glass Dynamics","domain":"math.PR","origin":"ai-generated","source":"hexagon","authors":["P. M. Aronow","Patrick Lopatto"],"reviews":0,"subject":"math.PR","summary":"We study Langevin dynamics for the pure spherical $p$-spin glass with $p\\ge3$, with covariance $Nq^p$ and generator $\\Delta_S+\\beta\\nabla_SH_N\\cdot\\nabla_S$, started from a uniform point independent of the disorder. We let the dimension tend to infinity on fixed time horizons and study the long-time behavior of the resulting hard-spherical Cugliandolo–Kurchan equations for the correlation $C$ and the response $R$. At every positive temperature, their solution has a unique stationary limit at bounded time differences, which satisfies the fluctuation–dissipation theorem (FDT), and its energy…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus","ChatGPT","ChatGPT"],"discussed":0,"published":"2026-10-11","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":true,"formalizations":["https://palomar-registry.org/entry?id=PALOMAR-2026-10-12-000002&version=1"],"human_understanding":"some"}