PreprintCC BY-NC-ND 4.0HAL
Cutoff beyond non-negative curvature
Abstract
We study how a relaxed gradient estimate is enough to prove cutoff for several new families of Markov processes, within the varentropy framework of [Sal25a].
In particular, we show how certain regularization estimates from hypocoercivity theory allow one to prove cutoff for kinetic dynamics. Moreover, we prove cutoff for some families of diffusions with non-convex potentials and for mean-field dynamics, as well as for biased random walks on the symmetric group, giving a simple proof of a far-reaching extension of a result of [NY24].
Related
- Torus actions, almost non-negative curvature and fundamental groups
- Restriction estimates for surfaces with negative curvature in ℝ3
- A remark on the compactness of manifolds with non-negative Ricci curvature and uniformly convex boundary
- Maximal symmetry rank and almost non-negative curvature in low dimensions
- Positivity of the canonical bundle and Hermitian metrics with quasi-negative holomorphic sectional curvature
BibTeX
@misc{fathi2026cutoff,
title = {{Cutoff beyond non-negative curvature}},
author = {Max Fathi and Arnaud Guillin and Cyril Labbé and Justin Salez},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26019},
eprint = {2610.26019},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05803728v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Cutoff beyond non-negative curvature
AU - Max Fathi
AU - Arnaud Guillin
AU - Cyril Labbé
AU - Justin Salez
PY - 2026
DA - 2026/10/16
PB - HAL
DO - 10.48550/arxiv.2610.26019
UR - https://hal.science/hal-05803728v1
AB - We study how a relaxed gradient estimate is enough to prove cutoff for several new families of Markov processes, within the varentropy framework of [Sal25a]. In particular, we show how certain regularization estimates from hypocoercivity theory allow one to prove cutoff for kinetic dynamics. Moreover, we prove cutoff for some families of diffusions with non-convex potentials and for mean-field dynamics, as well as for biased random walks on the symmetric group, giving a simple proof of a far-reaching extension of a result of [NY24].
ER -