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

   
@article{EJP2361,
	author = {Charles Bordenave},
	title = {Extinction probability and total progeny of predator-prey dynamics on infinite trees},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {19},
	year = {2014},
	keywords = {SIR models, predator-prey dynamics, branching processes},
	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.
},
	pages = {no. 20, 1-33},
	issn = {1083-6489},
	doi = {10.1214/EJP.v19-2361},    
        url = {http://ejp.ejpecp.org/article/view/2361}}