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Sesqui-type branching processes
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Univ Oxford, Math Inst, Radcliffe Observ Quarter, Woodstock Rd, Oxford OX2 6GG, England.
Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA;Univ Cambridge Peterhouse, Cambridge CB2 1RD, England.
2018 (English)In: Stochastic Processes and their Applications, ISSN 0304-4149, E-ISSN 1879-209X, Vol. 128, no 11, p. 3628-3655Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2018. Vol. 128, no 11, p. 3628-3655
Keywords [en]
Sesqui-type branching processes, Survival probability, Point probability
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-370017DOI: 10.1016/j.spa.2017.12.007ISI: 000447816800002OAI: oai:DiVA.org:uu-370017DiVA, id: diva2:1275673
Funder
Knut and Alice Wallenberg FoundationAvailable from: 2019-01-07 Created: 2019-01-07 Last updated: 2019-01-07Bibliographically approved

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Janson, Svante

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