Passage time of the frog model has a sublinear variance

Abstract : In this paper, we show that the passage time in the frog model on Z d with d ≥ 2 has a sublinear variance. The proof is based on the method introduced in [8] combining with tessellation arguments to estimate the martingale difference. We also apply this method to get the linearity of the lengths of optimal paths.
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https://hal.archives-ouvertes.fr/hal-01999031
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Submitted on : Wednesday, January 30, 2019 - 3:06:52 AM
Last modification on : Monday, March 4, 2019 - 2:04:22 PM

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van Hao Can, Shuta Nakajima. Passage time of the frog model has a sublinear variance. 2019. ⟨hal-01999031⟩

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