PreprintCC BY 4.0arXiv
Universality of cutoff for the Exclusion Process
Abstract
Under a fairly general condition on the underlying jump rates, we prove that the Exclusion Process with fixed particle density exhibits cutoff at time tmix∼ 1/2trel log N, where N is the volume and trel the relaxation time of the single-particle dynamics. Our result covers, in particular, the standard setting of uniform nearest-neighbor jumps on large discrete tori in any fixed dimension and, more generally, on any sequence of vertex-transitive graphs with bounded degree and polynomially diverging diameter. Our (short and entirely human) proof combines Wilson's method, the Octopus Inequality, Fourier analysis on Hamming slices, and a sharp comparison with the Dirichlet form of a natural accelerated variant of the dynamics.
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BibTeX
@misc{hermon2026universality,
title = {{Universality of cutoff for the Exclusion Process}},
author = {Jonathan Hermon and Gady Kozma and Justin Salez},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.31187},
eprint = {2609.31187},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31187},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Universality of cutoff for the Exclusion Process
AU - Jonathan Hermon
AU - Gady Kozma
AU - Justin Salez
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2609.31187
UR - https://arxiv.org/abs/2609.31187
AB - Under a fairly general condition on the underlying jump rates, we prove that the Exclusion Process with fixed particle density exhibits cutoff at time t_mix∼ 1/2t_rel log N, where N is the volume and t_rel the relaxation time of the single-particle dynamics. Our result covers, in particular, the standard setting of uniform nearest-neighbor jumps on large discrete tori in any fixed dimension and, more generally, on any sequence of vertex-transitive graphs with bounded degree and polynomially diverging diameter. Our (short and entirely human) proof combines Wilson's method, the Octopus Inequality, Fourier analysis on Hamming slices, and a sharp comparison with the Dirichlet form of a natural accelerated variant of the dynamics.
ER -