Fluctuations of the Magnetization for Ising models on Erdős-Rényi random graphs – the regimes of low temperature and external magnetic field

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2020-12-15 DOI:10.30757/alea.v19-21

Z. Kabluchko, Matthias Lowe, K. Schubert

引用次数: 4

Abstract

We continue our analysis of Ising models on the (directed) Erdős-Renyi random graph $G(N,p)$. We prove a quenched Central Limit Theorem for the magnetization and describe the fluctuations of the log-partition function. In the current note we consider the low temperature regime $\beta>1$ and the case when an external magnetic field is present. In both cases, we assume that $p=p(N)$ satisfies $p^3N \to \infty$.

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Erdős-Rényi随机图上Ising模型磁化的波动——低温和外磁场的状态

我们继续分析(有向)Erdős-Renyi随机图$G(N,p)$上的Ising模型。我们证明了磁化的一个淬灭中心极限定理，并描述了对数配分函数的涨落。在当前的说明中，我们考虑低温状态$\beta>1$和存在外部磁场的情况。在这两种情况下，我们都假设$p=p(N)$满足$p^3N \to \infty$。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Alea-Latin American Journal of Probability and Mathematical Statistics STATISTICS & PROBABILITY-

CiteScore

1.10

自引率

0.00%

发文量

期刊介绍： ALEA publishes research articles in probability theory, stochastic processes, mathematical statistics, and their applications. It publishes also review articles of subjects which developed considerably in recent years. All articles submitted go through a rigorous refereeing process by peers and are published immediately after accepted. ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs. Authors are allowed to deposit their published article into their institutional repository, freely and with no embargo, as long as they acknowledge the source of the paper. ALEA is affiliated with the Institute of Mathematical Statistics.