The branching capacity has been introduced by Zhu [Ann. Inst. Henri Poincare Probab. Stat. 57 (2021), pp. 73-93] as the limit of the hitting probability of a symmetric branching random walk in Zd, d >= 5. Similarly, we define the Brownian snake capacity in Rd, 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.

Publication:

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

http://dx.doi.org/10.1090/tran/9640

Author:Tianyi Bai

Chinese Academy of Sciences, China

Email address: tianyi.bai73@amss.ac.cn

Jean-François Delmas

CERMICS, Ecole des Ponts, France

Email address: delmas@cermics.enpc.fr

Yueyun Hu, LAGA

Université Paris XIII, 99 av. J.B. Clément, 93430 Villetaneuse, France

Email address: yueyun@math.univ-paris13.fr