Branching capacity and Brownian snake capacity
Abstract
The branching capacity has been introduced by Zhu [Ann. Inst. Henri Poincaré Probab. Stat. 57 (2021), pp. 73–93] as the limit of the hitting probability of a symmetric branching random walk in Z d \mathbb {Z}^{d} , d ≥ 5 d\ge 5 . Similarly, we define the Brownian snake capacity in R d \mathbb {R}^{d} , as the scaling limit of the hitting probability by the Brownian snake starting from afar. Then, we prove our main result on the vague convergence of the rescaled branching capacity towards this Brownian snake capacity. Our proof relies on a precise convergence rate for the approximation of the branching capacity by hitting probabilities.
Fields of Study & Subjects
Amphibian and Reptile Biology
Publication details
- Journal / source
- Transactions of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Volume
- 379
- Issue
- 9
- Pages
- 6167–6201
- Publication date
- 14 April 2026
- Language
- EN