On the tail of the branching random walk local time

Omer Angel; Tom Hutchcroft; Antal Jarai

doi:10.1007/s00440-020-01014-4

On the tail of the branching random walk local time

Omer Angel, Tom Hutchcroft, Antal Jarai

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Abstract

Consider a critical branching random walk on Z^d, d ≥ 1, started with a single particle at the origin, and let L(x) be the total number of particles that ever visit a vertex x. We study the tail of L(x) under suitable conditions on the offspring distribution. In particular, our results hold if the offspring distribution has an exponential moment.

Original language	English
Pages (from-to)	467-494
Number of pages	28
Journal	Probability Theory and Related Fields
Volume	180
Early online date	6 Nov 2020
DOIs	https://doi.org/10.1007/s00440-020-01014-4
Publication status	Published - 30 Jun 2021

Funding

The authors are grateful to the organizers of the Oberwolfach Workshop Strongly Correlated Interacting Processes, where this work was initiated. We thank Ed Perkins and Jean-François Le Gall for helpful discussions on the literature. OA is supported in part by an NSERC discovery Grant.

ASJC Scopus subject areas

General Mathematics

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10.1007/s00440-020-01014-4Licence: CC BY

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AB - Consider a critical branching random walk on Zd, d ≥ 1, started with a single particle at the origin, and let L(x) be the total number of particles that ever visit a vertex x. We study the tail of L(x) under suitable conditions on the offspring distribution. In particular, our results hold if the offspring distribution has an exponential moment.

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JO - Probability Theory and Related Fields

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On the tail of the branching random walk local time

Abstract

Funding

ASJC Scopus subject areas

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