Electronic Communications in Probability

Divergence of non-random fluctuation in First Passage Percolation

Shuta Nakajima

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We study the non-random fluctuation in first passage percolation and show that it diverges. We also prove the divergence of non-random shape fluctuation, which was predicted in [Yu Zhang. The divergence of fluctuations for shape in first passage percolation. Probab. Theory. Related. Fields. 136(2) 298–320, 2006].

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Electron. Commun. Probab., Volume 24 (2019), paper no. 65, 13 pp.

Received: 16 July 2018
Accepted: 19 September 2019
First available in Project Euclid: 31 October 2019

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Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

random environment first passage time fluctuation

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Nakajima, Shuta. Divergence of non-random fluctuation in First Passage Percolation. Electron. Commun. Probab. 24 (2019), paper no. 65, 13 pp. doi:10.1214/19-ECP267. https://projecteuclid.org/euclid.ecp/1572509099

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