Fine asymptotics of the magnetization of the annealed dilute Curie-Weiss model

Fuente: arXiv
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Main Authors: Apostel, Fabian, Döring, Hanna, Schubert, Kristina
Format: Preprint
Published: 2026
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author Apostel, Fabian
Döring, Hanna
Schubert, Kristina
author_facet Apostel, Fabian
Döring, Hanna
Schubert, Kristina
contents We consider the dilute Curie-Weiss model of size $N$, which is a generalization of the classical Curie-Weiss model where the dependency structure between the spins is not encoded by the complete graph but via the (directed) Erdős-Rényi graph on $N$ vertices in which every edge appears independently with probability $p(N)$. In the high temperature with external magnetic field regime ($0<β<1,h\in\mathbb{R}$) we prove for $p^{3}N^{2}\to\infty$ sharp cumulant bounds for the magnetization for the annealed Gibbs measure implying a central limit theorem with rate, a moderate deviation principle, a concentration inequality, a normal approximation bound with Cramér correction and mod-Gaussian convergence.
format Preprint
id arxiv_https___arxiv_org_abs_2603_09672
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Fine asymptotics of the magnetization of the annealed dilute Curie-Weiss model
Apostel, Fabian
Döring, Hanna
Schubert, Kristina
Probability
Mathematical Physics
60F10, 82B44, 82B20
We consider the dilute Curie-Weiss model of size $N$, which is a generalization of the classical Curie-Weiss model where the dependency structure between the spins is not encoded by the complete graph but via the (directed) Erdős-Rényi graph on $N$ vertices in which every edge appears independently with probability $p(N)$. In the high temperature with external magnetic field regime ($0<β<1,h\in\mathbb{R}$) we prove for $p^{3}N^{2}\to\infty$ sharp cumulant bounds for the magnetization for the annealed Gibbs measure implying a central limit theorem with rate, a moderate deviation principle, a concentration inequality, a normal approximation bound with Cramér correction and mod-Gaussian convergence.
title Fine asymptotics of the magnetization of the annealed dilute Curie-Weiss model
topic Probability
Mathematical Physics
60F10, 82B44, 82B20
url https://arxiv.org/abs/2603.09672