Minima in branching random walks
| Autor: | Louigi Addario-Berry, Bruce Reed |
|---|---|
| Přispěvatelé: | Monteil, Alain, Algorithms, simulation, combinatorics and optimization for telecommunications (MASCOTTE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-COMmunications, Réseaux, systèmes Embarqués et Distribués (Laboratoire I3S - COMRED), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS) |
| Jazyk: | angličtina |
| Rok vydání: | 2007 |
| Předmět: |
Statistics and Probability
60G50 branching processes 01 natural sciences Combinatorics Branching (linguistics) 010104 statistics & probability Branching random walks [INFO.INFO-MC]Computer Science [cs]/Mobile Computing [INFO.INFO-NI]Computer Science [cs]/Networking and Internet Architecture [cs.NI] Probability theory [INFO.INFO-MC] Computer Science [cs]/Mobile Computing Branching random walk Position (vector) FOS: Mathematics Mathematics - Combinatorics 0101 mathematics Mathematics 60J80 [INFO.INFO-NI] Computer Science [cs]/Networking and Internet Architecture [cs.NI] 010102 general mathematics Probability (math.PR) 16. Peace & justice Random walk Exponential function Maxima and minima Bounded function 60J80 (Primary) 60G50 (Secondary) Combinatorics (math.CO) Statistics Probability and Uncertainty random trees Mathematics - Probability |
| Zdroj: | Annals of Probability Annals of Probability, 2009, 37, pp.1044―1079 Ann. Probab. 37, no. 3 (2009), 1044-1079 Annals of Probability, Institute of Mathematical Statistics, 2009, 37, pp.1044―1079 |
| ISSN: | 0091-1798 2168-894X |
| Popis: | Given a branching random walk, let $M_n$ be the minimum position of any member of the $n$th generation. We calculate $\mathbf{E}M_n$ to within O(1) and prove exponential tail bounds for $\mathbf{P}\{|M_n-\mathbf{E}M_n|>x\}$, under quite general conditions on the branching random walk. In particular, together with work by Bramson [Z. Wahrsch. Verw. Gebiete 45 (1978) 89--108], our results fully characterize the possible behavior of $\mathbf {E}M_n$ when the branching random walk has bounded branching and step size. Published in at http://dx.doi.org/10.1214/08-AOP428 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org) |
| Databáze: | OpenAIRE |
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