Fluctuations of the Magnetization for Ising Models on Dense Erdős–Rényi Random Graphs
Fluctuations of the Magnetization for Ising Models on Dense Erdős–Rényi Random Graphs
复制标题
密集 Erdős-Rényi 随机图上 Ising 模型磁化强度的涨落
DOI：
10.1007/s10955-019-02358-5
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发表时间：
2019
影响因子：
1.6
通讯作者：
K. Schubert
中科院分区：
文献类型：
--
作者：
Z. Kabluchko;Matthias Löwe;K. Schubert
We analyze Ising/Curie–Weiss models on the (directed) Erdős–Rényi random graph on N vertices in which every edge is present with probability p. These models were introduced by Bovier and Gayrard (J Stat Phys 72(3–4):643–664, 1993). We prove a quenched Central Limit Theorem for the magnetization in the high-temperature regime β<1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta <1$$\end{document} when p=p(N)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p=p(N)$$\end{document} satisfies p3N2→+∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p^3N^2\rightarrow +\,\infty $$\end{document}.
We analyze Ising/Curie–Weiss models on the (directed) Erdős–Rényi random graph on N vertices in which every edge is present with probability p. These models were introduced by Bovier and Gayrard (J Stat Phys 72(3–4):643–664, 1993). We prove a quenched Central Limit Theorem for the magnetization in the high-temperature regime β<1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta <1$$\end{document} when p=p(N)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p=p(N)$$\end{document} satisfies p3N2→+∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p^3N^2\rightarrow +\,\infty $$\end{document}.
非齐次居里-维斯模型和退火随机图的临界行为
影响因子：
2.4
作者：
S. Dommers;C. Giardina;C. Giberti;R. van der Hofstad;M. L. Prioriello
通讯作者：
M. L. Prioriello