Sesqui-type branching processes |
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Authors: | Svante Janson Oliver Riordan Lutz Warnke |
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Affiliation: | 1. Department of Mathematics, Uppsala University, PO Box 480, SE-751 06 Uppsala, Sweden;2. Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK;3. School of Mathematics, Georgia Institute of Technology, Atlanta GA 30332, USA;4. Peterhouse, Cambridge CB2 1RD, UK |
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Abstract: | We consider branching processes consisting of particles (individuals) of two types (type and type ) in which only particles of type 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. |
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Keywords: | Sesqui-type branching processes Survival probability Point probability 60J80 |
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