Discrete Random Walks, DRW'03
Cyril Banderier and Christian Krattenthaler (eds.)
DMTCS Conference Volume AC (2003), pp. 325332
author:  Valentin Topchii and Vladimir Vatutin 

title:  Individuals at the origin in the critical catalytic branching random walk 
keywords:  catalytic branching random walk; critical twodimensional BellmanHarris process 
abstract: 
A continuous time branching random walk on the lattice
Z
is considered in which individuals may produce
children at the origin only. Assuming that the underlying
random walk is symmetric and the offspring reproduction law
is critical we prove a conditional limit theorem for the
number of individuals at the origin.

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reference:  Valentin Topchii and Vladimir Vatutin (2003), Individuals at the origin in the critical catalytic branching random walk, in Discrete Random Walks, DRW'03, Cyril Banderier and Christian Krattenthaler (eds.), Discrete Mathematics and Theoretical Computer Science Proceedings AC, pp. 325332 
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