A spectral condition for spectral gap: fast mixing in high-temperature Ising models
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Abstract
We prove that Ising models on the hypercube with general quadratic interactions satisfy a Poincaré inequality with respect to the natural Dirichlet form corresponding to Glauber dynamics, as soon as the operator norm of the interaction matrix is smaller than 1. The inequality implies a control on the mixing time of the Glauber dynamics. Our techniques rely on a localization procedure which establishes a structural result, stating that Ising measures may be decomposed into a mixture of measures with quadratic potentials of rank one, and provides a framework for proving concentration bounds for high temperature Ising models.
Date issued
2021-08-20Department
Massachusetts Institute of Technology. Department of MathematicsPublisher
Springer Berlin Heidelberg
Citation
Eldan, Ronen, Koehler, Frederic and Zeitouni, Ofer. 2021. "A spectral condition for spectral gap: fast mixing in high-temperature Ising models."
Version: Author's final manuscript