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May 2020 Oriented first passage percolation in the mean field limit
Nicola Kistler, Adrien Schertzer, Marius A. Schmidt
Braz. J. Probab. Stat. 34(2): 414-425 (May 2020). DOI: 10.1214/18-BJPS422

Abstract

The Poisson clumping heuristic has lead Aldous to conjecture the value of the oriented first passage percolation on the hypercube in the limit of large dimensions. Aldous’ conjecture has been rigorously confirmed by Fill and Pemantle (Ann. Appl. Probab. 3 (1993) 593–629) by means of a variance reduction trick. We present here a streamlined and, we believe, more natural proof based on ideas emerged in the study of Derrida’s random energy models.

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Nicola Kistler. Adrien Schertzer. Marius A. Schmidt. "Oriented first passage percolation in the mean field limit." Braz. J. Probab. Stat. 34 (2) 414 - 425, May 2020. https://doi.org/10.1214/18-BJPS422

Information

Received: 1 August 2018; Accepted: 1 October 2018; Published: May 2020
First available in Project Euclid: 4 May 2020

zbMATH: 07232936
MathSciNet: MR4093266
Digital Object Identifier: 10.1214/18-BJPS422

Rights: Copyright © 2020 Brazilian Statistical Association

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Vol.34 • No. 2 • May 2020
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