Fine asymptotics of the magnetization of the annealed dilute Curie-Weiss model
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| Format: | Preprint |
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2026
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| _version_ | 1866911503222833152 |
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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 |
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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 |