Poisson convergence and poisson processes with applications to random graphs

Svante Janson

Stochastic Processes and their Applications, 1987, vol. 26, 1-30

Abstract: We give a new sufficient condition for convergence to a Poisson distribution of a sequence of sums of dependent variables. The condition allows each summand to depend strongly on a few of the other variables and to depend weakly on the remaining ones. As a consequence we obtain sufficient conditions for the convergence of point processes, constructed as sets of (weakly) dependent random points in some space S, to a Poisson process. The main applications are to random graph theory. In particular, we solve the problem (proposed by Erdös) of finding the size of the first cycle in a random graph.

Keywords: Poisson; limits; Poisson; processes; point; processes; random; graphs; cycles; subgraph; statistics (search for similar items in EconPapers)
Date: 1987
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Citations: View citations in EconPapers (2)

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