Probability and Real Trees

École d'Été de Probabilités de Saint-Flour XXXV - 2005

  • Steven Neil Evans

Part of the Lecture Notes in Mathematics book series (LNM, volume 1920)

About this book

Introduction

Random trees and tree-valued stochastic processes are of particular importance in combinatorics, computer science, phylogenetics, and mathematical population genetics. Using the framework of abstract "tree-like" metric spaces (so-called real trees) and ideas from metric geometry such as the Gromov-Hausdorff distance, Evans and his collaborators have recently pioneered an approach to studying the asymptotic behaviour of such objects when the number of vertices goes to infinity. These notes survey the relevant mathematical background and present some selected applications of the theory.

Keywords

Combinatorics Dirichlet form Fractal Gromov-Hausdorff distance Markov process Stochastic processes coalescent continuum random tree stochastic process vertices

Authors and affiliations

  • Steven Neil Evans
    • 1
  1. 1.University of California at Berkeley94720-3860BerkeleyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-74798-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-74797-0
  • Online ISBN 978-3-540-74798-7
  • Series Print ISSN 0075-8434
  • About this book