{"id":"openai-math/A-spectral-gap-throughout-the-high-temperature-Sherrington-Kirkpatrick-phase","pdf":"https://github.com/openai/math/blob/main/preprints/A-spectral-gap-throughout-the-high-temperature-Sherrington-Kirkpatrick-phase-September-24-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-spectral-gap-throughout-the-high-temperature-Sherrington-Kirkpatrick-phase-September-24-2026","tags":["spin-glasses","markov-chains","mixing-times"],"score":0,"title":"A spectral gap throughout the high-temperature Sherrington–Kirkpatrick phase","domain":"Probability and statistical mechanics","family":"227","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"For every fixed inverse temperature $`0\\lt \\beta\\lt 1`$, we prove that the unscaled spectral gap of single-site heat-bath dynamics for the zero-field Gaussian Sherrington–Kirkpatrick model is bounded away from zero with probability tending to one over the disorder. Equivalently, the Gibbs law satisfies a dimension-free Poincaré inequality for all functions.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Critical SK autocorrelation processes and dynamics across the temperature transition"}