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

Ronen Eldan
Ronen Eldan
Ofer Zeitouni
Ofer Zeitouni
Cited by: 0|Views3

Abstract:

We prove that Ising models on the hypercube with general quadratic interactions satisfy a Poincar\'{e} 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 dyn...More

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