PreprintCC BY 4.0arXiv
On overlap concentration in the Curie-Weiss Random Field model
Abstract
We show that the overlaps of two independent replicas drawn from the Gibbs measure of the Curie--Weiss model with random field (CWRF) exhibit sub-Gaussian tails when the inverse temperature $ β< 1$ and the random field is drawn from a Gaussian distribution that makes the expected magnetization of the CWRF equal to its expected overlap in the thermodynamic limit. To show this, we prove finite-moment concentration via a rigorous Laplace approximation for a certain random rate function, and ``bootstrap'' it to a uniform bound for the moment-generating function of the squared overlap deviations using a sharp analysis of the associated rate function.
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BibTeX
@misc{li2026overlap,
title = {{On overlap concentration in the Curie-Weiss Random Field model}},
author = {Yutong Li and Juspreet Singh Sandhu and Jonathan Shi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08169},
eprint = {2609.08169},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08169},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On overlap concentration in the Curie-Weiss Random Field model
AU - Yutong Li
AU - Juspreet Singh Sandhu
AU - Jonathan Shi
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08169
UR - https://arxiv.org/abs/2609.08169
AB - We show that the overlaps of two independent replicas drawn from the Gibbs measure of the Curie--Weiss model with random field (CWRF) exhibit sub-Gaussian tails when the inverse temperature $ β< 1$ and the random field is drawn from a Gaussian distribution that makes the expected magnetization of the CWRF equal to its expected overlap in the thermodynamic limit. To show this, we prove finite-moment concentration via a rigorous Laplace approximation for a certain random rate function, and ``bootstrap'' it to a uniform bound for the moment-generating function of the squared overlap deviations using a sharp analysis of the associated rate function.
ER -