Sesqui-type branching processes
Probability
2018-11-02 v2 Combinatorics
Abstract
We consider branching processes consisting of particles (individuals) of two types (type L and type S) in which only particles of type L have offspring, proving estimates for the survival probability and the (tail of) the distribution of the total number of particles. Such processes are in some sense closer to single- than to multi-type branching processes. Nonetheless, the second, barren, type complicates the analysis significantly. The results proved here (about point and survival probabilities) are a key ingredient in the analysis of bounded-size Achlioptas processes in a recent paper by the last two authors.
Keywords
Cite
@article{arxiv.1706.00283,
title = {Sesqui-type branching processes},
author = {Svante Janson and Oliver Riordan and Lutz Warnke},
journal= {arXiv preprint arXiv:1706.00283},
year = {2018}
}
Comments
23 pages. References updated