Catalytic branching random walk with semi-exponential increments

Ekaterina Vl Bulinskaya

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In a catalytic branching random walk on a multidimensional lattice, with arbitrary finite total number of catalysts, in supercritical regime, when the vector coordinates of the random walk jump are assumed independent (or close to independent) to one another and have semi-exponential distributions, a limit theorem provides the almost sure normalized locations of the particles at the boundary between populated and empty areas. Contrary to the case of random walk increments with light distribution tails, the normalizing factor grows faster than linearly over time. The limit shape of the front in the case of semi-exponential tails is no longer convex, as it is in the case of light tails.

Original languageEnglish
Pages (from-to)1-31
Number of pages31
JournalMathematical Population Studies
Early online date11 Jul 2020
DOIs
Publication statusPublished - 2020
Externally publishedYes

Keywords

  • Catalytic branching random walk
  • heavy tails
  • propagation front
  • propagation of population
  • semi-exponential distribution tails
  • supercritical regime
  • NUMBER
  • SPREAD

OECD FOS+WOS

  • 5.04.FU DEMOGRAPHY
  • 1.01.PO MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
  • 5.04.PS SOCIAL SCIENCES, MATHEMATICAL METHODS
  • 1.01.XY STATISTICS & PROBABILITY
  • 5.07.JB ENVIRONMENTAL STUDIES

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