The Spread of a Catalytic Branching Random Walk

2012/02/03 by Philippe Carmona, Carmona, Philippe, Yueyun Hu +1
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1202.0637

34 pages, submitted

arxiv created 2012/09/27 · arxiv updated 2012/09/28

Abstract

We consider a random walk on \Z that branches at the origin only. In the supercritical regime we establish a law of large number for the maximal position M_n. Then we determine all possible limiting law for the sequence M_n -αn where α is a deterministic constant.

Related

• On the maximal displacement of catalytic branching random walk
• Branching random walk with a random environment in time
• Limiting laws of supercritical branching random walks
• On the boundary at infinity for branching random walk
• Limit theorems for the empirical distribution of supercritical branching random walks on transitive graphs