{"id":"openai-math/Functional-universality-of-critical-SK-autocorrelations","pdf":"https://github.com/openai/math/blob/main/preprints/Functional-universality-of-critical-SK-autocorrelations-October-5-2026/critical-sk-autocorrelations.pdf","url":"https://github.com/openai/math/tree/main/preprints/Functional-universality-of-critical-SK-autocorrelations-October-5-2026","tags":["spin-glasses","stochastic-dynamics","probability"],"score":0,"title":"Functional universality of critical SK autocorrelations","domain":"Probability and statistical mechanics","family":"227","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We prove that the stationary spin autocorrelation of the zero-field Sherrington–Kirkpatrick model at inverse temperature β = 1 has a common functional scaling limit for Gaussian and Rademacher couplings. With rate-one heat-bath clocks at every site, time is scaled by n 2/3 and the mean spin autocorrelation is multiplied by n 1/3 . The functions converge in law uniformly on compact positive-time intervals. Their limiting law is not a point mass: it retains sample-to-sample randomness, and its functions decay to zero at large times.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Critical SK autocorrelation processes and dynamics across the temperature transition"}