Zakhar Kabluchko, Matthias Löwe, Kristina Schubert
Published 2020-02-26Version 1
We analyze Ising/Curie-Weiss models on the Erd\H{o}s-R\'enyi graph with $N$ vertices and edge probability $p=p(N)$ that were introduced by Bovier and Gayrard [J.\ Statist.\ Phys., 72(3-4):643--664, 1993] and investigated in two previous articles by the authors. We prove Central Limit Theorems for the partition function of the model and -- at other decay regimes of $p(N)$ -- for the logarithmic partition function. We find critical regimes for $p(N)$ at which the behavior of the fluctuations of the partition function changes.
Variance asymptotics and central limit theorems for generalized growth processes with applications to convex hulls and maximal points
Central Limit Theorems for Radial Random Walks on $p\times q$ Matrices for $p\to\infty$
Central limit theorems for hyperbolic spaces and Jacobi processes on $[0,\infty[$
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