Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4589787 | Journal of Functional Analysis | 2016 | 40 Pages |
Abstract
We generalise the coarse Ricci curvature method of Ollivier by considering the coarse Ricci curvature of multiple steps in the Markov chain. This implies new spectral bounds and concentration inequalities. We also extend this approach to the bounds for MCMC empirical averages obtained by Joulin and Ollivier. We prove a recursive lower bound on the coarse Ricci curvature of multiple steps in the Markov chain, making our method broadly applicable. Applications include the split-merge random walk on partitions, Glauber dynamics with random scan and systemic scan for statistical physical spin models, and random walk on a binary cube with a forbidden region.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Daniel Paulin,