ANNEALED LIMIT THEOREMS FOR THE ISING MODEL ON RANDOM REGULAR GRAPHS

ANNEALED LIMIT THEOREMS FOR THE ISING MODEL ON RANDOM REGULAR GRAPHS

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...

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Veröffentlicht in:The Annals of applied probability 2019-06, Vol.29 (3), p.1398-1445
1. Verfasser: Can, Van Hao
Format: Artikel
Sprache:eng
Schlagworte:
Annealing
Graphs
Ising model
Mathematical models
Mathematics
Pressure
Probability
Proof theory
Random variables
Theorems
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Zusammenfassung: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.
ISSN:1050-5164
2168-8737
DOI:10.1214/17-AAP1377