scholarly journals An upper bound for the probability of visiting a distant point by a critical branching random walk in $\mathbb{Z} ^{4}$

2019 ◽  
Vol 24 (0) ◽  
Author(s):  
Qingsan Zhu
Keyword(s):  
Random Walk ◽  
Upper Bound ◽  
Branching Random Walk ◽  
Distant Point ◽  
Critical Branching Random Walk

scholarly journals On the tail of the branching random walk local time

2020 ◽  
Author(s):  
Omer Angel ◽  
Tom Hutchcroft ◽  
Antal Járai
Keyword(s):  
Random Walk ◽  
Local Time ◽  
Single Particle ◽  
Branching Random Walk ◽  
Exponential Moment ◽  
Offspring Distribution ◽  
Critical Branching Random Walk ◽  
Number Of Particles

Abstract Consider 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.

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