Quantitative dependence of the Pierrehumbert flow's mixing rate on the amplitude
Dynamical Systems
2025-11-11 v2 Probability
Abstract
We quantitatively study the mixing rate of randomly shifted alternating shears on the torus. This flow was introduced by Pierrehumbert '94, and was recently shown to be exponentially mixing. In this work, we quantify the dependence of the exponential mixing rate on the flow amplitude. Our approach is based on constructing an explicit Lyapunov function and a coupling trajectory for the associated two-point Markov chain, together with an application of the quantitative Harris theorem.
Keywords
Cite
@article{arxiv.2510.27686,
title = {Quantitative dependence of the Pierrehumbert flow's mixing rate on the amplitude},
author = {Seungjae Son},
journal= {arXiv preprint arXiv:2510.27686},
year = {2025}
}