Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Divergence of shape fluctuation for general distributions in first-passage percolation

Shuta Nakajima

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Abstract

We study the shape fluctuation in the first-passage percolation on $\mathbb{Z}^{d}$. It is known that it diverges when the distribution obeys Bernoulli in Zhang (Probab. Theory. Related. Fields. 136 (2006) 298–320). In this paper, we extend the result to general distributions.

Résumé

Nous étudions les fluctuations de la forme limite pour la percolation de premier passage dans $\mathbb{Z}^{d}$. Il est connu que ces fluctuations divergent dans le cas des lois de Bernoulli [Zhang (Probab. Theory. Related. Fields. 136 (2006) 298–320)]. Dans cet article, nous étendons ce résultat à toutes les lois.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 56, Number 2 (2020), 782-791.

Dates
Received: 8 May 2018
Revised: 17 February 2019
Accepted: 21 March 2019
First available in Project Euclid: 16 March 2020

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1584345619

Digital Object Identifier
doi:10.1214/19-AIHP982

Mathematical Reviews number (MathSciNet)
MR4076765

Subjects
Primary: 60K37: Processes in random environments
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82A51

Keywords
Random environment First-passage percolation Shape fluctuation

Citation

Nakajima, Shuta. Divergence of shape fluctuation for general distributions in first-passage percolation. Ann. Inst. H. Poincaré Probab. Statist. 56 (2020), no. 2, 782--791. doi:10.1214/19-AIHP982. https://projecteuclid.org/euclid.aihp/1584345619


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