Branching capacity of a random walk in \mathbb Z⁵

2024/04/30 by Bai, Tianyi, Delmas, Jean-François, Hu, Yueyun
#60F05 #60J45 #60J80 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2404.19447

Abstract

We are interested in the branching capacity of the range of a random walk in \mathbb Z^d.Schapira [28] has recently obtained precise asymptotics in the case d≥ 6 and has demonstrated a transition at dimension d=6. We study the case d=5 and prove that the renormalized branching capacity converges in law to the Brownian snake capacity of the range of a Brownian motion. The main step in the proof relies on studying the intersection probability between the range of a critical Branching random walk and that of a random walk, which is of independent interest.

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