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PreprintCC BYarXiv (Cornell University)

A simple proof of rapid mixing on random regular graphs beyond uniqueness

  • Andreas Göbel
  • Matthew Jenssen
  • Marcus Michelen
  • Marcus Pappik
  • Will Perkins
  • Leon Schiller
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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 L2-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.

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Cite

BibTeXRIS
BibTeX
@misc{gobel2026simple,
  title = {{A simple proof of rapid mixing on random regular graphs beyond uniqueness}},
  author = {Andreas Göbel and Matthew Jenssen and Marcus Michelen and Marcus Pappik and Will Perkins and Leon Schiller},
  howpublished = {arXiv (Cornell University)},
  year = {2026},
  month = jun,
  doi = {10.48550/arxiv.2606.27545},
  url = {https://arxiv.org/abs/2606.27545},
  note = {CC BY},
}
RIS
TY  - UNPB
TI  - A simple proof of rapid mixing on random regular graphs beyond uniqueness
AU  - Andreas Göbel
AU  - Matthew Jenssen
AU  - Marcus Michelen
AU  - Marcus Pappik
AU  - Will Perkins
AU  - Leon Schiller
PY  - 2026
DA  - 2026/06/25
PB  - arXiv (Cornell University)
DO  - 10.48550/arxiv.2606.27545
UR  - https://arxiv.org/abs/2606.27545
AB  - 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.
SN  - 2331-8422
ER  -