Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Transversal fluctuations for a first passage percolation model

Yuri Bakhtin and Wei Wu

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Abstract

In 1996, Licea, Newman, and Piza proved that for a rather convoluted definition of the transversal fluctuation exponent in first passage percolation, that exponent is bounded below by $3/5$. In this paper we introduce a new first passage percolation model in a Poissonian environment on $\mathbb{R}^{2}$, and prove the same estimate for a natural clean notion of the exponent.

Résumé

En 1996, Licea, Newman et Piza ont démontré que, pour une définition plutôt compliquée de l’exposant de la fluctuation transversale en percolation de premier passage, cet exposant est borné inférieurement par $3/5$. Dans cet article, nous introduisons un nouveau modèle de percolation de premier passage dans un environnement poissonien sur $\mathbb{R}^{2}$ et démontrons la même estimée pour une notion naturelle de l’exposant.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 55, Number 2 (2019), 1042-1060.

Dates
Received: 12 November 2016
Revised: 17 January 2018
Accepted: 16 April 2018
First available in Project Euclid: 14 May 2019

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1557820841

Digital Object Identifier
doi:10.1214/18-AIHP908

Mathematical Reviews number (MathSciNet)
MR3949963

Zentralblatt MATH identifier
07097341

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B43: Percolation [See also 60K35]

Keywords
First passage percolation Transversal fluctuation Poissonian potential Superdiffusivity

Citation

Bakhtin, Yuri; Wu, Wei. Transversal fluctuations for a first passage percolation model. Ann. Inst. H. Poincaré Probab. Statist. 55 (2019), no. 2, 1042--1060. doi:10.1214/18-AIHP908. https://projecteuclid.org/euclid.aihp/1557820841


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