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Journal Article
SPATIAL GROWTH PROCESSES WITH LONG RANGE DISPERSION
2020
Overview
We consider the speed of propagation of a continuous-time continuousspace branching random walk with the additional restriction that the birth rate at any spatial point cannot exceed 1. The dispersion kernel is taken to have density that decays polynomially as |x|−2α, x → ∞. We show that if α >2, then the system spreads at a linear speed, while for
α
∈
(
1
2
,
2
]
the spread is faster than linear. We also consider the mesoscopic equation corresponding to the microscopic stochastic system. We show that in contrast to the microscopic process, the solution to the mesoscopic equation spreads exponentially fast for every
α
>
1
2
.
Publisher
Institute of Mathematical Statistics
Subject
