# Random Walks and Trees

ESAIM: Proceedings (2011)

- Volume: 31, page 1-39
- ISSN: 1270-900X

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topShi, 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 -

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