Maximum of a catalytic branching random walk

Bulinskaya, E. Vl.

doi:10.1070/rm9885

Cited by 5 publications

(3 citation statements)

References 8 publications

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“…Thus, statement ( 14) is proved. Inequality (15) follows from the proven inequality (14) and the definition of the function Λ.…”

Section: Proof Of the Main Resultsmentioning

confidence: 99%

“…To estimate the integral J 1 (t) apply inequality (15) to the integrand for values t large enough, which results in…”

Section: Lemma 2 Let Conditionsmentioning

confidence: 99%

“…The study of the population spread in supercritical CBRW from another view-point of the almost sure convergence was initiated in paper [18] for d = 1 and for "light" distribution tails of the random walk. This investigation was developed in the series of the author's works [15], [12]- [17] under assumptions of d > 1 and "heavy" distribution tails of the walk jump.…”

Section: Introductionmentioning

confidence: 99%

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Fluctuations of the Propagation Front of a Catalytic Branching Walk

Bulinskaya¹

2020

Theory Probab. Appl.

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We consider a supercritical catalytic branching random walk (CBRW) on a multidimensional lattice Z d , d ∈ N. 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 M n of the particles at time n. They proved that M n /n → µ almost surely (on a set of local non-degeneracy of CBRW), as n → ∞, where µ > 0 is a certain constant. Under additional assumption of a single catalyst in CBRW they also investigated the fluctuations of M n with respect to µn, as n → ∞. 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 Z d . 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.

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“…Thus, statement ( 14) is proved. Inequality (15) follows from the proven inequality (14) and the definition of the function Λ.…”

Section: Proof Of the Main Resultsmentioning

confidence: 99%

“…To estimate the integral J 1 (t) apply inequality (15) to the integrand for values t large enough, which results in…”

Section: Lemma 2 Let Conditionsmentioning

confidence: 99%