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Kistler, Nicola; Schertzer, Adrien; Schmidt, Marius A.

Oriented first passage percolation in the mean field limit. (English) Zbl 1453.60159

Braz. J. Probab. Stat. 34, No. 2, 414-425 (2020).
Summary: 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 J. A. Fill and R. Pemantle [Ann. Appl. Probab. 3, No. 2, 593–629 (1993; Zbl 0783.60102)] 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.

Cited in 1 Review

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
05C80 Random graphs (graph-theoretic aspects)
82B43 Percolation

Keywords:

first passage percolation; mean field approximation; Derrida’s REMs

Citations:

Zbl 0783.60102
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\textit{N. Kistler} et al., Braz. J. Probab. Stat. 34, No. 2, 414--425 (2020; Zbl 1453.60159)
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References:

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[2] Arguin, L.-P. (2016). Extrema of log-correlated random variables: Principles and examples. In Advances in Disordered Systems, Random Processes and Some Applications (P. Contucci and C. Giardiná, eds.). Cambridge: Cambridge Univiersity Press.
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[9] Kistler, N. (2015). Derrida’s random energy models. From spin glasses to the extremes of correlated radom fields. In Correlated Random Systems: Five Different Methods (V. Gayrard and N. Kistler, eds.), Lecture Notes in Mathematics 2143. Cham: Springer. · Zbl 1338.60231
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