Abstract
AbstractConsider a critical branching random walk on $$\mathbb Z^d$$
Z
d
, $$d\ge 1$$
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.
Funder
Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada
Publisher
Springer Science and Business Media LLC
Subject
Statistics, Probability and Uncertainty,Statistics and Probability,Analysis
Reference24 articles.
1. Aizenman, M., Newman, C.M.: Tree graph inequalities and critical behavior in percolation models. J. Stat. Phys. 36(1–2), 107–143 (1984)
2. Benjamini, I., Curien, N.: Recurrence of the $${\mathbb{Z}}^d$$-valued infinite snake via unimodularity. Electron. Commun. Probab. 17(1), 10 (2012)
3. Bhupatiraju, S., Hanson, J., Járai, A.: Inequalities for critical exponents in $$ d $$-dimensional sandpiles. Preprint arXiv:1602.06475, (2016)
4. Dhar, D.: Self-organized critical state of sandpile automaton models. Phys. Rev. Lett. 64(14), 1613–1616 (1990)
5. Hutchcroft, T.: Universality of high-dimensional spanning forests and sandpiles. Probab. Theory Relat. Fields 176, 1–65 (2018)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献