2019/08/14 by Ekaterina Vl. Bulinskaya, E. Vl. Bulinskaya
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #advanced mathematical theories #math.PR #msc:60F05 #msc:60J80
paper · pdf · doi:10.1137/s0040585x97t989672
published as Theory of Probability and its Applications, vol.64(2019), no.4, pp.513--534
arxiv created 2019/08/14 · crossref issued 2020/01/01 · crossref published 2020/01/01 · crossref published-print 2020/01/01 · openalex publication_date 2020/01/01 · crossref published-online 2020/02/13 · crossref created 2020/02/13 · crossref deposited 2020/02/13 · arxiv updated 2020/07/14 · openalex created_date 2025/10/10 · crossref indexed 2026/07/27 · openalex updated_date 2026/07/28
We consider a supercritical catalytic branching random walk (CBRW) on a multidimensional lattice Zd (d is positive integer). The main subject of study is the behavior of particles cloud in space and time. For CBRW on an integer line, Carmona and Hu (2014) examined the asymptotical behavior of the maximal coordinate Mn of the particles at time n. They proved that Mn/n converges to μalmost surely (on a set of local non-degeneracy of CBRW), as n tends to infinity, where μ>0 is a certain constant. Under additional assumption of a single catalyst in CBRW they also investigated the fluctuations of Mn with respect to μn, as n grows to infinity. Bulinskaya (2018) extended the strong limit theorem by Carmona and Hu having estimated the rate of the population propagation for the front of a multidimensional CBRW. Now our aim is to analyze fluctuations of the propagation front in CBRW on Zd. We not only solve the problem in a multidimensional setting but also, treating the case of an arbitrary finite number of catalysts for d = 1, generalize the result by Carmona and Hu with the help of other probabilistic-analytic methods. Keywords and phrases: catalytic branching random walk, supercritical regime, spread of population, propagation front, fluctuations of front.