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A spatial zero-one law for equilibria of branching particle systems (1993)

Matthes, K. ; Siegmund-Schultze, R. ; Wakolbinger, A.

Springer

Journal of theoretical probability 6 (1993), S. 699-711

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ISSN: 1572-9230

Keywords: Branching particle systems ; equilibrium distributions ; random point measures ; zero-one law on spatial tail field

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract We prove that a large class of equilibria of branching particle systems (namely those which arise as an independent superposition of a Poisson system of “clans,” or equivalently, as a limit distribution of the branching process started off from a Poisson system of particles with invariant intensity measure) obey a zero-one law on the σ-algebra of remote events (or spatial tial field), provided only that the meannth generation offspring numbers of single particle are uniformly bounded.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01049172

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