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We consider an age-dependent branching particle system in ℝ,
where the particles are subject to -stable migration
(0 < ≤ 2), critical binary branching, and
general (non-arithmetic) lifetimes distribution. The population starts off from a Poisson
random field in ℝ with Lebesgue intensity. We prove
functional central limit theorems and strong laws of large numbers under two rescalings:
high particle density, and a space-time rescaling...
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