Electronic Communications in Probability

First passage percolation on the exponential of two-dimensional branching random walk

Jian Ding and Subhajit Goswami

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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 $O(N^{1 - \gamma ^2/10})$.

Article information

Electron. Commun. Probab., Volume 22 (2017), paper no. 69, 14 pp.

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

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Zentralblatt MATH identifier

Primary: 60G15: Gaussian processes

first passage percolation (FPP) branching random walk (BRW) Gaussian free field (GFF) Liouville quantum gravity (LQG)

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Ding, Jian; Goswami, Subhajit. First passage percolation on the exponential of two-dimensional branching random walk. Electron. Commun. Probab. 22 (2017), paper no. 69, 14 pp. doi:10.1214/17-ECP102. https://projecteuclid.org/euclid.ecp/1514451624

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