Year: 2025
Type: article
Abstract: We are interested in the branching capacity of the range of a random walk in Zd. Schapira [29] 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.
DOI: 10.1214/25-ejp1334
Authors: Tianyi Bai, Jean-François Delmas, Yueyun Hu
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $675
OpenAlex ID: W4409566567