Corpus ID: 220546472

A Spectral Condition for Spectral Gap: Fast Mixing in High-Temperature Ising Models

@article{Eldan2020ASC,
  title={A Spectral Condition for Spectral Gap: Fast Mixing in High-Temperature Ising Models},
  author={Ronen Eldan and Frederic Koehler and O. Zeitouni},
  journal={arXiv: Probability},
  year={2020}
}
We prove that Ising models on the hypercube with general quadratic interactions satisfy a Poincare 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… Expand
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