arXiv
Open Access
2024
Branching capacity of a random walk in $\mathbb Z^5$
Tianyi Bai
Jean-François Delmas
Yueyun Hu
Abstrak
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 $d\ge 6$ 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.
Topik & Kata Kunci
Penulis (3)
T
Tianyi Bai
J
Jean-François Delmas
Y
Yueyun Hu
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2024
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓