Concentration inequalities and Transfer operators for supercritical Dyson models

2025/08/03 by Mirmukhsin Makhmudov, Makhmudov, Mirmukhsin · 1 citation
Mathematics · #37A50 #37A60 #37C30 #60G60 #82B05 #82B20 #82B26 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2508.01703

openalex publication_date 2025/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The present paper extends the results on the ferromagnetic Dyson models from \citesEFMV2024, 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.

Citations

• On an extension of a theorem by Ruelle to long-range potentials
• The Eigenfunctions of the Transfer Operator for the Dyson model in a field
• Continuous eigenfunctions of the transfer operator for Dyson models
• A New Correlation Inequality for Ising Models with External Fields
• Phase transitions in long-range Ising models and an optimal condition for factors of g-measures
• Ruelle Operator for Continuous Potentials and DLR-Gibbs Measures
• Decay of the Two-Point Function in One-Dimensional O(N) Spin Models with Long-Range Interactions

Cited by

• Equality of the critical inverse temperatures for the one- and two-sided Dyson models

Related

• Critical phenomena in the Dyson hierarchical model and renormalization group
• Dyson models under renormalization and in weak fields
• Continuous eigenfunctions of the transfer operator for Dyson models
• Decimation of the Dyson-Ising Ferromagnet
• Concentration via metastable mixing, with applications to the supercritical exponential random graph model