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Extinction probability and total progeny of predator-prey dynamics on infinite trees


 
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1. Title Title of document Extinction probability and total progeny of predator-prey dynamics on infinite trees
 
2. Creator Author's name, affiliation, country Charles Bordenave; Université de Toulouse & CNRS
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) SIR models, predator-prey dynamics, branching processes
 
3. Subject Subject classification 60J80.
 
4. Description Abstract

We consider the spreading dynamics of two nested invasion clusters on an infinite tree. This model was defined as the chase-escape model by Kordzakhia and it admits a limit process, the birth-and-assassination process, previously introduced by Aldous and Krebs. On both models, we prove an asymptotic equivalent of the extinction probability near criticality. In the subcritical regime, we give a tail bound on the total progeny of the preys before extinction.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2014-02-07
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2361
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-2361
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
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