A new Stein-method-based Gaussian approximation controls the full correlation structure of Ising models with a single negative eigenvalue outlier, delivering near-optimal mixing times where prior spectral methods break down.
Polynomial mixing of the critical ising model on sparse erdos-renyi graphs
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Proves polynomial mixing of Glauber dynamics at the antiferromagnetic two-spin uniqueness threshold and optimal logarithmic mixing for Swendsen-Wang dynamics on bounded-degree graphs, resolving a conjecture.
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Fast mixing in Ising models with a negative spectral outlier via Gaussian approximation
A new Stein-method-based Gaussian approximation controls the full correlation structure of Ising models with a single negative eigenvalue outlier, delivering near-optimal mixing times where prior spectral methods break down.
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Edge-Tilting Field Dynamics: Rapid Mixing at the Uniqueness Threshold and Optimal Mixing for Swendsen-Wang Dynamics
Proves polynomial mixing of Glauber dynamics at the antiferromagnetic two-spin uniqueness threshold and optimal logarithmic mixing for Swendsen-Wang dynamics on bounded-degree graphs, resolving a conjecture.