Branching Random Walks

École d'Été de Probabilités de Saint-Flour XLII – 2012

AvZhan Shi

Häftad, Engelska, 2016

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2016-02-05
Mått:155 x 235 x 11 mm
Vikt:242 g
Format:Häftad
Språk:Engelska
Serie:Lecture Notes in Mathematics
Antal sidor:133
Förlag:Springer International Publishing AG
ISBN:9783319253718

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Recensioner i media

"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)

Innehållsförteckning

I Introduction.- II Galton–Watson trees.- III Branching random walks and martingales.- IV The spinal decomposition theorem.- V Applications of the spinal decomposition theorem.- VI Branching random walks with selection.- VII Biased random walks on Galton–Watson trees.- A Sums of i.i.d. random variables.- References.