The Annals of Applied Probability

Annealed limit theorems for the Ising model on random regular graphs

Van Hao Can

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Abstract

In a recent paper, Giardinà et al. [ALEA Lat. Am. J. Probab. Math. Stat. 13 (2016) 121–161] have proved a law of large number and a central limit theorem with respect to the annealed measure for the magnetization of the Ising model on some random graphs, including the random 2-regular graph. In this paper, we present a new proof of their results which applies to all random regular graphs. In addition, we prove the existence of annealed pressure in the case of configuration model random graphs.

Article information

Source
Ann. Appl. Probab., Volume 29, Number 3 (2019), 1398-1445.

Dates
Received: May 2017
Revised: September 2017
First available in Project Euclid: 19 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1550566834

Digital Object Identifier
doi:10.1214/17-AAP1377

Mathematical Reviews number (MathSciNet)
MR3914548

Zentralblatt MATH identifier
07057458

Subjects
Primary: 05C80: Random graphs [See also 60B20] 60F5
Secondary: 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs

Keywords
Ising model random graphs central limit theorems annealed measure

Citation

Can, Van Hao. Annealed limit theorems for the Ising model on random regular graphs. Ann. Appl. Probab. 29 (2019), no. 3, 1398--1445. doi:10.1214/17-AAP1377. https://projecteuclid.org/euclid.aoap/1550566834


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