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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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.


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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

First passage percolation Transversal fluctuation Poissonian potential Superdiffusivity


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.

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