Capacity of the range of tree-indexed random walk
نویسندگان
چکیده
By introducing a new measure for the infinite Galton–Watson process and providing estimates (discrete) Green’s functions on trees, we establish asymptotic behavior of capacity critical branching random walks: in high dimensions d≥7, grows linearly; dimension d=6, it asymptotically proportional to nlogn.
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ژورنال
عنوان ژورنال: Annals of Applied Probability
سال: 2022
ISSN: ['1050-5164', '2168-8737']
DOI: https://doi.org/10.1214/21-aap1689