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arXiv · 2506.22258

Mixing Time Bounds for the Gibbs Sampler under Isoperimetry

Alexander Goyal·George Deligiannidis·Nikolas Kantas
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Abstract

We establish bounds on the conductance for the systematic-scan and random-scan Gibbs samplers when the target distribution satisfies a Poincar\'e or log-Sobolev inequality and possesses sufficiently regular conditional distributions. These bounds lead to mixing time guarantees that extend beyond the log-concave setting, offering new insights into the convergence behavior of Gibbs sampling in broader regimes. Moreover, we demonstrate that our results remain valid for log-Lipschitz and log-smooth target distributions. Our approach relies on novel isoperimetric inequalities and a sequential coupling argument for the Gibbs sampler.

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Alexander Goyal, George Deligiannidis, Nikolas Kantas. 2025-06-27. Mixing Time Bounds for the Gibbs Sampler under Isoperimetry. https://arxiv.org/abs/2506.22258

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