A lower bound for the spectral gap of the conjugate Kac process with 3 interacting particles
Mathematical Physics
2021-07-20 v1 math.MP
Abstract
In this paper, we proceed as suggested in the final section of arXiv:1812.03874v2 and prove a lower bound for the spectral gap of the conjugate Kac process with 3 interacting particles. This bound turns out to be around , which is already physically meaningful, and we perform Monte Carlo simulations to provide a better empirical estimate for this value via entropy production inequalities. This finishes a complete quantitative estimate of the spectral gap of the Kac process.
Keywords
Cite
@article{arxiv.2107.08275,
title = {A lower bound for the spectral gap of the conjugate Kac process with 3 interacting particles},
author = {Luís Simão Ferreira},
journal= {arXiv preprint arXiv:2107.08275},
year = {2021}
}