Open Access
2019 First passage time of the frog model has a sublinear variance
Van Hao Can, Shuta Nakajima
Electron. J. Probab. 24: 1-27 (2019). DOI: 10.1214/19-EJP334


In this paper, we show that the first passage time in the frog model on $\mathbb{Z} ^{d}$ with $d\geq 2$ has a sublinear variance. This implies that the central limit theorem does not hold at least with the standard diffusive scaling. The proof is based on the method introduced in [4, 11] combined with a control of the maximal weight of paths in a locally dependent site-percolation. We also apply this method to get the linearity of the lengths of optimal paths.


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Van Hao Can. Shuta Nakajima. "First passage time of the frog model has a sublinear variance." Electron. J. Probab. 24 1 - 27, 2019.


Received: 1 October 2018; Accepted: 15 June 2019; Published: 2019
First available in Project Euclid: 5 July 2019

zbMATH: 07089014
MathSciNet: MR3978226
Digital Object Identifier: 10.1214/19-EJP334

Primary: 60J10 , 60J80 , 60K35

Keywords: First passage time , frog model , sublinear variance

Vol.24 • 2019
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