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.
Exponentially slow mixing of the low temperature SK model
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Proves an exponential lower bound on the mixing time of Glauber dynamics for the p-spin glass at inverse temperatures above C ln(p)/p for large p, via energy landscape analysis with Gaussian decompositions and a bottleneck bound.
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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.