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May 2020 Divergence of shape fluctuation for general distributions in first-passage percolation
Shuta Nakajima
Ann. Inst. H. Poincaré Probab. Statist. 56(2): 782-791 (May 2020). DOI: 10.1214/19-AIHP982

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.

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.

Citation

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Shuta Nakajima. "Divergence of shape fluctuation for general distributions in first-passage percolation." Ann. Inst. H. Poincaré Probab. Statist. 56 (2) 782 - 791, May 2020. https://doi.org/10.1214/19-AIHP982

Information

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

zbMATH: 07199879
MathSciNet: MR4076765
Digital Object Identifier: 10.1214/19-AIHP982

Subjects:
Primary: 60K37
Secondary: 60K35, 82A51

Rights: Copyright © 2020 Institut Henri Poincaré

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Vol.56 • No. 2 • May 2020
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