Year: 2026
Type: preprint
Abstract: A recent breakthrough of Chen, Chen, Chen, Yin, and Zhang shows rapid mixing for Glauber dynamics for the hard-core model on random regular graphs beyond the tree uniqueness threshold. Their approach builds upon the literature of various local-to-global techniques and applies to a more general setting of discrete distributions supported on downward-closed set families. We give a short and self-contained proof via a Bochner--Bakry--Émery approach and directly show a Poincaré inequality by expanding the Dirichlet form in terms of the $L^2$-norm of the generator applied to a test function and eliminating a sum of squares term. Our proof is a streamlined version of an argument of Kondratiev, Kuna, and Ohlerich used to study spatial birth-and-death dynamics for Gibbs point processes in the continuum, which we adapt to the discrete setting.
Source: arXiv (Cornell University)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166562581