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arXiv · 2211.14188

Spectral Gap Inequalities on Nilpotent Lie Groups in Infinite Dimensions

Esther Bou Dagher·Yaozhong Qiu·Boguslaw Zegarlinski·Mengchun Zhang
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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.

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Esther Bou Dagher, Yaozhong Qiu, Boguslaw Zegarlinski, Mengchun Zhang. 2022-11-25. Spectral Gap Inequalities on Nilpotent Lie Groups in Infinite Dimensions. https://arxiv.org/abs/2211.14188

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