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Branching Processes with Negative Offspring Distributions
Ioana Dumitriu1, Joel Spencer2, and Catherine Yan3
1Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
dumitriu@math.mit.edu
2Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
spencer@cims.nyu.edu
3Department of Mathematics, Texas A & M University, College Station, TX 77843, USA
cyan@math.tamu.edu
Annals of Combinatorics 7 (1) p.35-47 March, 2003
AMS Subject Classification: 05A16, 05D40, 60J80
Abstract:
A branching process is a mathematical description of the growth of a population for which the individual produces offsprings according to stochastic laws. Branching processes can be modeled by one-dimensional random walks with non-negative integral step-sizes. In this paper we consider the random walk with a similar algebraic setting but the step-size distribution is allowed to take negative values. We gave the exact formula for the limit probability under which the random walk continues forever. Asymptotic results are also presented.
Keywords: branching processes, negative offsprings

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