On the tail of the branching random walk local time
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.
Additional InformationThe 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.
Submitted - 2002.12188.pdf