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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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.


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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

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

Random environment First-passage percolation Shape fluctuation


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.

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