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arXiv · 1804.03117

First passage percolation in the mean field limit

Nicola Kistler·Adrien Schertzer·Marius A. Schmidt
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Abstract

The Poisson clumping heuristic has lead Aldous to conjecture the value of the first passage percolation on the hypercube in the limit of large dimensions. Aldous' conjecture has been rigorously confirmed by Fill and Pemantle [Annals of Applied Prob- ability 3 (1993)] 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. 2018-04-09. First passage percolation in the mean field limit. https://arxiv.org/abs/1804.03117

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