Volume 31, January 2011X Symposium on Probability and Stochastic Processes and the First Joint Meeting France-Mexico of Probability
|Page(s)||1 - 39|
|Published online||15 March 2011|
Random Walks and Trees
Université Paris VI, Laboratoire de Probabilités et Modèles
Aléatoires, 4 place Jussieu, 75252 Paris Cedex 05, France.
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  and to the forthcoming book of Lyons and Peres , as well as to Duquesne and Le Gall  and Le Gall  for continuous random trees.
© EDP Sciences, ESAIM 2011
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