Cutoff Phenomenon for the Glauber-Misanthrope process in a perturbative regime
Abstract
We investigate the Glauber--Misanthrope process, obtained by superposing a Misanthrope dynamics with finite site capacity and a Glauber dynamics which creates or annihilates particles one at a time at each site. In a perturbative regime around the diffusively scaled partial exclusion process, we prove the cutoff phenomenon and identify the limiting mixing time. Our approach relies on the information percolation framework developed by Lubetzky and Sly and extended by Tran, which we adapt to accommodate multiple occupancy per site and account for the two distinct correlation mechanisms generated by the Misanthrope and Glauber dynamics. Our lower bound on the mixing time holds under assumptions more general than those required for the matching upper bound.
Related
- Information Percolation and cutoff for Potts Glauber Dynamics
- Universality of cutoff for the Exclusion Process
- Canonical Local Equilibrium and Cutoff Profiles for the Symmetric Exclusion Process on Discrete Tori
- Glauber Dynamics for Sampling Colorings: Rapid Mixing above (1+1/e)Δ via Hidden Hard-Core Models
- Mixing profile for Glauber dynamics of the discrete Gaussian Free Field starting from super-harmonic functions
BibTeX
@misc{rameh2026cutoff,
title = {{Cutoff Phenomenon for the Glauber-Misanthrope process in a perturbative regime}},
author = {Ons Rameh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21898},
eprint = {2610.21898},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21898},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Cutoff Phenomenon for the Glauber-Misanthrope process in a perturbative regime
AU - Ons Rameh
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21898
UR - https://arxiv.org/abs/2610.21898
AB - We investigate the Glauber--Misanthrope process, obtained by superposing a Misanthrope dynamics with finite site capacity and a Glauber dynamics which creates or annihilates particles one at a time at each site. In a perturbative regime around the diffusively scaled partial exclusion process, we prove the cutoff phenomenon and identify the limiting mixing time. Our approach relies on the information percolation framework developed by Lubetzky and Sly and extended by Tran, which we adapt to accommodate multiple occupancy per site and account for the two distinct correlation mechanisms generated by the Misanthrope and Glauber dynamics. Our lower bound on the mixing time holds under assumptions more general than those required for the matching upper bound.
ER -