Spectral Gap Inequalities on Nilpotent Lie Groups in Infinite Dimensions
Functional Analysis
2022-11-28 v1 Probability
Abstract
We develop a general framework for spectral gap inequalities for Gibbs measures on infinite dimensional spin spaces over nilpotent Lie groups in terms of weak U-bounds and weak single-site spectral gap inequalities. We then provide sufficient conditions on the local specification and give examples of measures constructed using the Kaplan norm and generalising a few results for the Carnot-Caratheodory distance on the Heisenberg group.
Keywords
Cite
@article{arxiv.2211.14188,
title = {Spectral Gap Inequalities on Nilpotent Lie Groups in Infinite Dimensions},
author = {Esther Bou Dagher and Yaozhong Qiu and Boguslaw Zegarlinski and Mengchun Zhang},
journal= {arXiv preprint arXiv:2211.14188},
year = {2022}
}
Comments
37 pages, 6 sections