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2017 First passage percolation on the exponential of two-dimensional branching random walk
Jian Ding, Subhajit Goswami
Electron. Commun. Probab. 22: 1-14 (2017). DOI: 10.1214/17-ECP102

Abstract

We consider the branching random walk $\{\mathcal R^N_z: z\in V_N\}$ with Gaussian increments indexed over a two-dimensional box $V_N$ of side length $N$, and we study the first passage percolation where each vertex is assigned weight $e^{\gamma \mathcal R^N_z}$ for $\gamma >0$. We show that for $\gamma >0$ sufficiently small but fixed, the expected FPP distance between the left and right boundaries is at most $O(N^{1 - \gamma ^2/10})$.

Citation

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Jian Ding. Subhajit Goswami. "First passage percolation on the exponential of two-dimensional branching random walk." Electron. Commun. Probab. 22 1 - 14, 2017. https://doi.org/10.1214/17-ECP102

Information

Received: 19 October 2016; Accepted: 30 November 2017; Published: 2017
First available in Project Euclid: 28 December 2017

zbMATH: 06827051
MathSciNet: MR3742400
Digital Object Identifier: 10.1214/17-ECP102

Subjects:
Primary: 60G15

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