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SUMMARY:Poster Session - 
DTSTART:20241029T153000Z
DTEND:20241029T163000Z
UID:TALK220747@talks.cam.ac.uk
DESCRIPTION:The branching capacity has been proven by Zhu (2016) as the li
 mit of the hitting probability of a symmetric branching random walk in Z^d
 \, d &ge\; 5. Similarly\, we define the Brownian snake capacity in R^d\, a
 s the scaling limit of the hitting probability on the Brownian snake start
 ing from afar. We prove the vague convergence of the rescaled branching ca
 pacity towards this Brownian snake capacity. As an interesting example\, w
 e study the branching capacity of the range of a random walk in Z^d. Schap
 ira (2024) has recently obtained precise asymptotics in the case d &ge\; 6
  and has demonstrated a transition at dimension d = 6. We are interested i
 n the case d = 5 and prove that the renormalized branching capacity conver
 ges to the Brownian snake capacity of the range of a Brownian motion.\n&nb
 sp\;\nCo-authors: names and affiliations: Tianyi Bai (AMSS) and Jean-Fran&
 ccedil\;ois Delmas (CERMICS)\n&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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