Spectral Gap Inequalities on Nilpotent Lie Groups in Infinite Dimensions

Esther Bou Dagher, Yaozhong Qiu, Boguslaw Zegarlinski, Mengchun Zhang

Published 2022-11-25Version 1

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.