The genealogy of critical branching processes☆

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Abstract

In this paper we will obtain results concerning the distribution of generations and the degree of relationship of the individuals in a critical branching process {Z(t), t⩾0} and we will apply these results to obtain a “central limit theorem” for critical branching random walks.

MSC

Primary 60J80
Secondary 60F05

Keywords

critical branching process
generation numbers
degree of relationship
branching random walk
central limit theorem

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This research was supported by NSF Grant No. MCS 72-04591.

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