First passage percolation in the mean field limit

2018/04/09 by Nicola Kistler, Kistler, Nicola, Adrien Schertzer +3 · 1 citation
Mathematics · Physics and Astronomy · #60G70 #60J80 #82B44 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1804.03117

openalex publication_date 2018/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Minimum-Weight Path in a Sparse Erdős--Rényi Graph with Signed Weights

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