Poisson convergence and poisson processes with applications to random graphs
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.
Year of publication: |
1987
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Authors: | Janson, Svante |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 26.1987, p. 1-30
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Publisher: |
Elsevier |
Keywords: | Poisson limits Poisson processes point processes random graphs cycles subgraph statistics |
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