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- W4239285049 abstract "We consider a system of independent branching random walks on R which start from a Poisson point process with intensity of the form e λ (d u ) = e -λ u d u , where λ ∈ R is chosen in such a way that the overall intensity of particles is preserved. Denote by χ the cluster distribution, and let φ be the log-Laplace transform of the intensity of χ. If λφ'(λ) > 0, we show that the system is persistent, meaning that the point process formed by the particles in the n th generation converges as n → ∞ to a non-trivial point process Π e λ χ with intensity e λ . If λφ'(λ) < 0 then the branching population suffers local extinction, meaning that the limiting point process is empty. We characterize point processes on R which are cluster invariant with respect to the cluster distribution χ as mixtures of the point processes Π ce λ χ over c > 0 and λ ∈ K st , where K st = {λ ∈ R : φ(λ) = 0, λφ'(λ) > 0}." @default.
- W4239285049 created "2022-05-12" @default.
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- W4239285049 date "2012-03-01" @default.
- W4239285049 modified "2023-09-25" @default.
- W4239285049 title "Persistence and Equilibria of Branching Populations with Exponential Intensity" @default.
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- W4239285049 doi "https://doi.org/10.1017/s0021900200008962" @default.
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