Concentration inequalities and Transfer operators for supercritical Dyson models

TL;DR

This paper extends the analysis of ferromagnetic Dyson models to near-critical and strongly interacting regimes, establishing Gaussian concentration bounds for the infinite-volume Gibbs measure in the supercritical phase.

Contribution

It introduces new concentration inequalities for Dyson models in supercritical regimes, advancing understanding of their probabilistic behavior.

Findings

Gaussian concentration bounds for supercritical Dyson models

Extension of results to near-critical regimes

Analysis of infinite-volume Gibbs measure

Abstract

The present paper extends the results on the ferromagnetic Dyson models from \cites{EFMV2024, JOP2025} to the near-critical and strongly interacting regimes. As part of our main result, we further establish Gaussian concentration bounds for the unique infinite-volume Gibbs measure throughout the entire supercritical regime.