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Algebraic relaxation of random field Ising model dynamics

Published on:

10 November 2023

Primary Category:

Probability

Paper Authors:

Ahmed El Alaoui,

Ronen Eldan,

Reza Gheissari,

Arianna Piana

Bullets

Key Details

Studies Glauber dynamics for the random field Ising model

Proves algebraic relaxation under weak spatial mixing

Gives polynomial-time sampling algorithm from this

Shows exponential relaxation with strong spatial mixing

Combines stochastic localization and coarse-graining

AI generated summary

Algebraic relaxation of random field Ising model dynamics

This paper studies the Glauber dynamics for the random field Ising model on finite lattices. The main results are: (1) Under a weak spatial mixing assumption, the dynamics exhibit algebraic relaxation to equilibrium in polynomial time. This leads to a polynomial-time sampling algorithm. (2) With strong spatial mixing, exponential relaxation and mixing are proven. The proofs involve increasing field variance through stochastic localization, and controlling bad regions via field-dependent coarse-graining.

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