Random Walks and Trees

Shi, Zhan. Emilia Caballero, Ma., et al, eds. "Random Walks and Trees." ESAIM: Proceedings 31 (2011): 1-39. <http://eudml.org/doc/251224>.

@article{Shi2011,
abstract = {These notes provide an elementary and self-contained introduction to branching random walks. Section 1 gives a brief overview of Galton–Watson trees, whereas Section 2 presents the classical law of large numbers for branching random walks. These two short sections are not exactly indispensable, but they introduce the idea of using size-biased trees, thus giving motivations and an avant-goût to the main part, Section 3, where branching random walks are studied from a deeper point of view, and are connected to the model of directed polymers on a tree. Tree-related random processes form a rich and exciting research subject. These notes cover only special topics. For a general account, we refer to the St-Flour lecture notes of Peres [47] and to the forthcoming book of Lyons and Peres [42], as well as to Duquesne and Le Gall [23] and Le Gall [37] for continuous random trees.},
author = {Shi, Zhan},
editor = {Emilia Caballero, Ma., Chaumont, Loïc, Hernández-Hernández, Daniel, Rivero, Víctor},
journal = {ESAIM: Proceedings},
keywords = {branching random walks; Galton-Watson trees; law of large numbers; central limit theorem},
language = {eng},
month = {3},
pages = {1-39},
publisher = {EDP Sciences},
title = {Random Walks and Trees},
url = {http://eudml.org/doc/251224},
volume = {31},
year = {2011},
}

TY - JOUR
AU - Shi, Zhan
AU - Emilia Caballero, Ma.
AU - Chaumont, Loïc
AU - Hernández-Hernández, Daniel
AU - Rivero, Víctor
TI - Random Walks and Trees
JO - ESAIM: Proceedings
DA - 2011/3//
PB - EDP Sciences
VL - 31
SP - 1
EP - 39
AB - These notes provide an elementary and self-contained introduction to branching random walks. Section 1 gives a brief overview of Galton–Watson trees, whereas Section 2 presents the classical law of large numbers for branching random walks. These two short sections are not exactly indispensable, but they introduce the idea of using size-biased trees, thus giving motivations and an avant-goût to the main part, Section 3, where branching random walks are studied from a deeper point of view, and are connected to the model of directed polymers on a tree. Tree-related random processes form a rich and exciting research subject. These notes cover only special topics. For a general account, we refer to the St-Flour lecture notes of Peres [47] and to the forthcoming book of Lyons and Peres [42], as well as to Duquesne and Le Gall [23] and Le Gall [37] for continuous random trees.
LA - eng
KW - branching random walks; Galton-Watson trees; law of large numbers; central limit theorem
UR - http://eudml.org/doc/251224
ER -