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 language | English |
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Pages (from-to) | 1-31 |
Number of pages | 31 |
Journal | Mathematical Population Studies |
Early online date | 11 Jul 2020 |
DOIs | |
Publication status | Published - 2020 |
Externally published | Yes |
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