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Local Geometric Mixing via Dobrushin Contraction with Applications to Diffusion Path Monte Carlo and the Proximal Sampler

arXiv · AI, language, vision and robotics · article · Sep 23, 2026 · UTC

Local geometric mixing localizes geometric mixing by requiring geometric convergence to equilibrium in total variation only over finitely many transitions. It accommodates local convergence rates and captures rapid local equilibration, even when global mixing is much slower. We establish and discuss local geometric mixing bounds through Dobrushin contraction. We then apply this approach to Diffusion Path Monte Carlo, a recently proposed Markov chain Monte Carlo method, aimed at leveraging advances in score-based modeling, whose ideal transitions coincide with those of the Proximal Sampler. Our

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