Pith. sign in

REVIEW 1 cited by

Branching capacity and Brownian snake capacity

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

arxiv 2402.13735 v2 pith:FC2ZGY7Z submitted 2024-02-21 math.PR

classification math.PR
keywords capacitybranchingbrowniansnakehittingconvergencelimitmathbb
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

The branching capacity has been introduced by [Zhu 2016] as the limit of the hitting probability of a symmetric branching random walk in $\mathbb Z^d$, $d\ge 5$. Similarly, we define the Brownian snake capacity in $\mathbb R^d$, as the scaling limit of the hitting probability by the Brownian snake starting from afar. Then, we prove our main result on the vague convergence of the rescaled branching capacity towards this Brownian snake capacity. Our proof relies on a precise convergence rate for the approximation of the branching capacity by hitting probabilities.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Yaglom theorem for critical branching random walk on $\mathbb{Z}^d$

    math.PR 2025-12 conditional novelty 7.0 of 10

    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.

Pith tools