The precise tail behavior of the total progeny of a killed branching random walk
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Elie Aïdékon [1] ; Yueyun Hu [2] ; Olivier Zindy [3]
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[1] Eindhoven University of Technology
Eindhoven University of Technology
Países Bajos
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[2] Pierre and Marie Curie University
Pierre and Marie Curie University
París, Francia
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[3] Université Paris XIII
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- Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 6, 2013, págs. 3786-3878
- Idioma: inglés
- DOI: 10.1214/13-AOP842
- Texto completo no disponible (Saber más ...)
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Resumen
Consider a branching random walk on the real line with a killing barrier at zero: starting from a nonnegative point, particles reproduce and move independently, but are killed when they touch the negative half-line. The population of the killed branching random walk dies out almost surely in both critical and subcritical cases, where by subcritical case we mean that the rightmost particle of the branching random walk without killing has a negative speed, and by critical case, when this speed is zero. We investigate the total progeny of the killed branching random walk and give their precise tail distribution both in the critical and subcritical cases, which solves an open problem of Aldous [Power laws and killed branching random walks, http://www.stat.berkeley.edu/~aldous/Research/OP/brw.html].
