Journal
ANNALS OF APPLIED PROBABILITY
Volume 32, Issue 3, Pages 1557-1589Publisher
INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/21-AAP1689
Keywords
Galton-Watson tree; branching random walk; capacity of the range
Categories
Ask authors/readers for more resources
By introducing a new measure for the infinite Galton-Watson process and providing estimates for (discrete) Green's functions on trees, the authors establish the asymptotic behavior of the capacity of critical branching random walks: in high dimensions d >= 7, the capacity grows linearly; and in the critical dimension d = 6, it grows asymptotically proportional to n/log n.
By introducing a new measure for the infinite Galton-Watson process and providing estimates for (discrete) Green's functions on trees, we establish the asymptotic behavior of the capacity of critical branching random walks: in high dimensions d >= 7, the capacity grows linearly; and in the critical dimension d = 6, it grows asymptotically proportional to n/log n.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available