Local convergence of large random triangulations coupled with an Ising model - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Transactions of the American Mathematical Society Année : 2021

Local convergence of large random triangulations coupled with an Ising model

Résumé

We prove the existence of the local weak limit of the measure obtained by sampling random triangulations of size $ n$ decorated by an Ising configuration with a weight proportional to the energy of this configuration. To do so, we establish the algebraicity and the asymptotic behaviour of the partition functions of triangulations with spins for any boundary condition. In particular, we show that these partition functions all have the same phase transition at the same critical temperature. Some properties of the limiting object - called the Infinite Ising Planar Triangulation - are derived, including the recurrence of the simple random walk at the critical temperature.
Fichier principal
Vignette du fichier
Albenque_Menard_Schaeffer.pdf (889.68 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-02999826 , version 1 (04-01-2021)

Identifiants

Citer

Marie Albenque, Laurent Ménard, Gilles Schaeffer. Local convergence of large random triangulations coupled with an Ising model. Transactions of the American Mathematical Society, 2021, 374 (1), pp.175-217. ⟨10.1090/tran/8150⟩. ⟨hal-02999826⟩
57 Consultations
65 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More