Entropy-controlled Last-Passage Percolation - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue The Annals of Applied Probability Année : 2019

Entropy-controlled Last-Passage Percolation

Résumé

In the present article we consider a natural generalization of Hammersley's Last Passage Percolation (LPP) called Entropy-controlled Last Passage Percolation (E-LPP), where points can be collected by paths with a global (entropy) constraint which takes in account the whole structure of the path, instead of a local ($1$-Lipschitz) constraint as in Hammersley's LPP. The E-LPP turns out to be a key ingredient in the context of the directed polymer model when the environment is heavy-tailed, which we consider in the related paper [Berger and Torri, 2018]. We prove several estimates on the E-LPP in continuous and in discrete settings, which are of interest on their own. We give applications in the context of polymers in heavy-tail environment which are essentials tools in [Berger and Torri, 2018]: we show that the limiting variational problem conjectured by [Dey and Zygouras, 2016] (Conjecture 1.7) is finite, and we prove that the discrete variational problem converges to the continuous one, generalizing techniques used by [Auffinger and Louidor, 2011] and [Hambly and Martin, 2007].
Fichier principal
Vignette du fichier
EntropyControlled_arXiv3.pdf (337.01 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01811267 , version 1 (13-11-2018)

Identifiants

Citer

Quentin Berger, Torri Niccolo. Entropy-controlled Last-Passage Percolation. The Annals of Applied Probability, 2019, 29 (3), pp.1878-1903. ⟨hal-01811267⟩
73 Consultations
72 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More