Branching Random Walks

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

  • Zhan Shi

Part of the Lecture Notes in Mathematics book series (LNM, volume 2151)

Also part of the École d'Été de Probabilités de Saint-Flour book sub series (LNMECOLE, volume 2151)

Table of contents

  1. Front Matter
    Pages i-x
  2. Zhan Shi
    Pages 1-10
  3. Zhan Shi
    Pages 11-17
  4. Zhan Shi
    Pages 29-44
  5. Back Matter
    Pages 115-136

About this book

Introduction

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.     

Keywords

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

Authors and affiliations

  • Zhan Shi
    • 1
  1. 1.Lab Probabilités et Modèles AléatoiresUniversité Pierre et Marie CurieParis CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-25372-5
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-25371-8
  • Online ISBN 978-3-319-25372-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book