REVIEW 2 cited by
On the critical branching random walk I: Branching capacity and visiting probability
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
abstract
We extend the theory of discrete capacity to critical branching random walk. We introduce branching capacity for any finite subset of $\Z^d, d\geq5$. Analogous to the regular discrete capacity, branching capacity is closely related to the asymptotics of the probability of visiting a fixed finite set by a critical branching random walk starting from a distant point and the conditional distribution of the hitting point.
Forward citations
Cited by 2 Pith papers
-
Yaglom theorem for critical branching random walk on $\mathbb{Z}^d$
Conditioned on hitting a distant set K, the total occupation time of a critical branching random walk is of order ||x||^{4-d} for d≤3, log||x|| for d=4, and bounded for d≥5, with explicit weak limits in all dimensions.
-
On the intersection of critical percolation clusters and other tree-like random graphs
Stretched-exponential tail bounds for intersections of independent critical percolation clusters, incipient infinite clusters, and branching random walk ranges are proved with explicit exponents.
Discussion (0). Continue with ORCID to comment.