Passage time of the frog model has a sublinear variance

2019/04/07 by Van Hao Can, Can, Van Hao, Shuta Nakajima +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1904.03667

openalex publication_date 2019/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show that the first passage time in the frog model on \Z^d with d≥ 2 has a sublinear variance. This implies that the central limit theorem does not holds at least with the standard diffusive scaling. The proof is based on the method introduced in \citeBRo, DHS combining with a control of the maximal weight of paths in locally dependent site-percolation. We also apply this method to get the linearity of the lengths of optimal paths..

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