Branching Random Walks

Providing an elementary introduction to branching random walks, the main focus of these lecture notes is on the asymptotic properties of one-dimensional discrete-time supercritical branching random walks, and in particular, on extreme positions in each generation, as well as the evolution of these positions over time.

Starting with the simple case of Galton-Watson trees, the text primarily concentrates on exploiting, in various contexts, the spinal structure of branching random walks. The notes end with some applications to biased random walks on trees.

• 60J80,60J85,60G50 60K37
• branching processes
• random walks
• spinal decomposition
• extreme values
• processes in random environments

“The text is a very well and professionally written presentation of the recent developments in the field of BRW. By focusing on key aspects and results, it provides a perfect guide for any researcher in probability theory, especially those who are looking for a relatively quick introduction.” (Gerold Alsmeyer, Mathematical Reviews, December 2016) 

“The lecture notes under review provide an introduction to supercritical branching random walks (BRW). … These nice lecture notes introduce the reader into deep results on branching random walks obtained in the recent few years. The book will be useful to all specialists in probability theory.” (Zakhar Kabluchko, zbMATH 1348.60004, 2016)

• Lab Probabilités et Modèles Aléatoires, Université Pierre et Marie Curie, Paris Cedex, France

  Zhan Shi

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