2016/06/03 by Ekaterina Vl. Bulinskaya, E. Vl. Bulinskaya · 3 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · #Diffusion and Search Dynamics #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #math.PR #msc:60F15 #msc:60J80
paper · pdf · doi:10.1016/j.spa.2017.09.007
published as Stochastic Processes and Their Applications, vol.128(2018), no.7, pp.2325-2340 · 2 figures
arxiv created 2016/06/03 · openalex publication_date 2017/10/02 · arxiv updated 2018/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
For a supercritical catalytic branching random walk on Zd (d is positive integer) with an arbitrary finite catalysts set we study the spread of particles population as time grows to infinity. Namely, we divide by t the position coordinates of each particle existing at time t and then let t tend to infinity. It is shown that in the limit there are a.s. no particles outside the closed convex surface in Rd which we call the propagation front and, under condition of infinite number of visits of the catalysts set, a.s. there exist particles on the propagation front. We also demonstrate that the propagation front is asymptotically densely populated and derive its alternative representation. Recent strong limit theorems for total and local particles numbers established by the author play an essential role. The results obtained develop ones by Ph.Carmona and Y.Hu (2014) devoted to the spread of catalytic branching random walk on Z. Keywords and phrases: branching random walk, supercritical regime, spread of population, propagation front, many-to-one lemma.