Work

Branching random walk in random environment

Year: 2026

Type: preprint

Abstract: We consider a branching random walk on \(\Z^d\) in a random environment given by Bernoulli site percolation with parameter \(p\in (0,1)\). In this model, each particle located at an open site reproduces according to a law \(μ_\circ\), whereas a particle at a closed site reproduces according to another law \(μ_\bullet\). Each newly born child performs an independent simple random walk jump from the position of its parent. We study the quenched survival probability under various assumptions on \((μ_\circ, μ_\bullet)\) and establish a Yaglom theorem when both offspring distributions are critical.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.13084

Authors: Chen, Xinxin, Gu, Chenlin, Zhao, Zhiqi

Institutions: Beijing Normal University, Capital Normal University, Tsinghua University, University of Oxford

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Fundamental Research Funds for the Central Universities

Awards: G2306923292, G4301156662, G503841967, G592411391

OpenAlex ID: W7203475068

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