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Preprint in the OpenAI Math release

A spectral gap throughout the high-temperature Sherrington–Kirkpatrick phase

OpenAI

Abstract

For every fixed inverse temperature , 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.

open until 1 Jan 2028

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