Multidimensional catalytic branching random walk with regularly varying tails

Ekaterina Vl Bulinskaya

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

3 Citations (Scopus)

Abstract

Catalytic branching random walk (CBRW) describes reproduction of particles and their movement in space. The particles may give offspring in the presence of catalysts. Consider CBRW model where the particles perform a random walk over a multidimensional lattice, without procreation outside the catalysts. The latter take a finite number of fixed positions at the lattice. We study the particles spread in case of non-extinction of population initiated by a single particle. The rate of population spread depends essentially on the distribution tails of the random walk jumps. Consider the jumps with independent (or close to independent) components having regularly varying “heavy’’ tails. The main results show that, after a proper normalization of positions, in the time limit the particles concentrate on a random set, located at the coordinate axes. For a two-dimensional case, the limiting set forms a cross, and, for any higher dimension d, it is a collection of d segments containing the origin. The joint distribution of such segments lengths is found and the time-limit is understood in the sense of weak convergence. This radically differs from the known results for both the CBRW with “light” and semi-exponential distribution tails of the random walk jumps.

Original languageEnglish
Title of host publicationICoMS 2019 - Proceedings of 2019 2nd International Conference on Mathematics and Statistics
PublisherAssociation for Computing Machinery
Pages6-13
Number of pages8
ISBN (Electronic)9781450371681
DOIs
Publication statusPublished - 8 Jul 2019
Event2nd International Conference on Mathematics and Statistics, ICoMS 2019 - Prague, Czech Republic
Duration: 8 Jul 201910 Jul 2019

Publication series

NameACM International Conference Proceeding Series

Conference

Conference2nd International Conference on Mathematics and Statistics, ICoMS 2019
CountryCzech Republic
CityPrague
Period08.07.201910.07.2019

Keywords

  • Catalytic branching random walk
  • Heavy tails
  • Population front
  • Regularly varying tails
  • Spread of population
  • Supercritical regime

Fingerprint Dive into the research topics of 'Multidimensional catalytic branching random walk with regularly varying tails'. Together they form a unique fingerprint.

  • Cite this

    Bulinskaya, E. V. (2019). Multidimensional catalytic branching random walk with regularly varying tails. In ICoMS 2019 - Proceedings of 2019 2nd International Conference on Mathematics and Statistics (pp. 6-13). (ACM International Conference Proceeding Series). Association for Computing Machinery. https://doi.org/10.1145/3343485.3343493