TY - JOUR
T1 - On the critical branching random walk III
T2 - The critical dimension
AU - Zhu, Qingsan
N1 - Publisher Copyright:
© Association des Publications de l’Institut Henri Poincaré, 2021
PY - 2021/2
Y1 - 2021/2
N2 - In this paper, we study the critical branching random walk in the critical dimension, four. We provide the asymptotics of the probability of visiting a fixed finite set and the range of the critical branching random walk conditioned on the total number of offspring. We also prove that conditioned on visiting a finite set, the first visiting point converges in distribution, when the starting point tends to infinity.
AB - In this paper, we study the critical branching random walk in the critical dimension, four. We provide the asymptotics of the probability of visiting a fixed finite set and the range of the critical branching random walk conditioned on the total number of offspring. We also prove that conditioned on visiting a finite set, the first visiting point converges in distribution, when the starting point tends to infinity.
KW - Critical branching random walk
KW - Harmonic measure
KW - Range
KW - Tree-indexed random walk
KW - Visiting probability
UR - http://www.scopus.com/inward/record.url?scp=85104233748&partnerID=8YFLogxK
U2 - 10.1214/20-AIHP1071
DO - 10.1214/20-AIHP1071
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AN - SCOPUS:85104233748
SN - 0246-0203
VL - 57
SP - 73
EP - 93
JO - Annales de l'institut Henri Poincare (B) Probability and Statistics
JF - Annales de l'institut Henri Poincare (B) Probability and Statistics
IS - 1
ER -