MINIMA IN BRANCHING RANDOM WALKS

被引：90

作者：

Addario-Berry, Louigi ^{[1
]}

Reed, Bruce ^{[2
,3
]}

机构：

[1] Univ Montreal, Dept Math & Stat, Montreal, PQ H3C 3J7, Canada

[2] McGill Univ, Sch Comp Sci, Canada Res Chair, Montreal, PQ H3A 2A7, Canada

[3] INRIA, Equipe Mascotte, Labo 13S, Sophia Antipolis, France

来源：

ANNALS OF PROBABILITY | 2009年 / 37卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Branching random walks; branching processes; random trees; WEIGHTED HEIGHT; DISPLACEMENT; DEVIATIONS; POSITION;

D O I：

10.1214/08-AOP428

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Given a branching random walk, let M-n be the minimum position of any member of the nth generation. We calculate EMn to within O(1) and prove exponential tail bounds for P{vertical bar M-n - EMn vertical bar > 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 EMn when the branching random walk has bounded branching and step size.

引用

页码：1044 / 1079

页数：36

共 50 条

[41] Branching random walks on free products of groups
Candellero, Elisabetta
Gilch, Lorenz A.
Mueller, Sebastian
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2012, 104 : 1085 - 1120
[42] Occupation densities of ensembles of branching random walks
Lalley, Steven P.
Tang, Si
ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2020, 25
[43] The number of ends of critical branching random walks
Candellero, Elisabetta
Roberts, Matthew I.
ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2015, 12 (01): : 55 - 67
[44] Field Theory of Branching and Annihilating Random Walks
Cardy, J. L.
Taeuber, U. C.
Journal of Statistical Physics, 90 (1-2):
[45] Anisotropic branching random walks on homogeneous trees
Irene Hueter
Steven P. Lalley
Probability Theory and Related Fields, 2000, 116 : 57 - 88
[46] Simulation of Branching Random Walks on a Multidimensional Lattice
Ermishkina E.M.
Yarovaya E.B.
Journal of Mathematical Sciences, 2021, 254 (4) : 469 - 484
[47] A note on branching random walks on finite sets
Mountford, T
Schinazi, RB
JOURNAL OF APPLIED PROBABILITY, 2005, 42 (01) : 287 - 294
[48] ONE LIMIT THEOREM FOR BRANCHING RANDOM WALKS
Smorodina, N., V
Yarovaya, E. B.
THEORY OF PROBABILITY AND ITS APPLICATIONS, 2024, 68 (04) : 630 - 642
[49] Martingale method for studying branching random walks
Smorodina, N. V.
Yarovaya, E. B.
RUSSIAN MATHEMATICAL SURVEYS, 2022, 77 (05) : 955 - 957
[50] On the maximal displacement of subcritical branching random walks
Eyal Neuman
Xinghua Zheng
Probability Theory and Related Fields, 2017, 167 : 1137 - 1164

← 1 2 3 4 5 →