Central limit theorem for high temperature Ising models via martingale embedding

2025/11/09 by Fang, Xiao, Zhao, Yi-Kun
#60F05 #60J27 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2511.06196

Abstract

We use martingale embeddings to prove a central limit theorem (CLT) for projections of high-dimensional random vectors satisfying a Poincaré inequality. We obtain a non-asymptotic error bound for the CLT in 2-Wasserstein distance involving two-point and three-point covariances. We present two illustrative applications to Ising models: one with finite-range interactions and the other in the ferromagnetic case under the Dobrushin condition.

Citations

• Randomstrasse101: Open Problems of 2024
• Fluctuations in random field Ising models
• Trickle-Down in Localization Schemes and Applications
• Normal approximation for exponential random graphs
• A Spectral Condition for Spectral Gap: Fast Mixing in High-Temperature Ising Models
• Fluctuations in Mean-Field Ising models
• A Generalized Central Limit Conjecture for Convex Bodies
• Stability of the logarithmic Sobolev inequality via the Föllmer Process
• The CLT in high dimensions: quantitative bounds via martingale embedding
• Power-law estimates for the central limit theorem for convex sets

Related

• Central limit theorem for the free energy of the random field Ising\n model
• Fluctuations for block spin Ising models
• The CLT in high dimensions: quantitative bounds via martingale embedding
• A high dimensional Central Limit Theorem for martingales, with applications to context tree models
• Fluctuations of the Magnetization for Ising Models on Dense Erdős-Rényi Random Graphs