Steven Neil Evans (auth.)3540747974, 9783540747970
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.
Table of contents :
Front Matter….Pages I-XI
Introduction….Pages 1-8
Around the Continuum Random Tree….Pages 9-20
R-Trees and 0-Hyperbolic Spaces….Pages 21-44
Hausdorff and Gromov–Hausdorff Distance….Pages 45-68
Root Growth with Re-Grafting….Pages 69-86
The Wild Chain and other Bipartite Chains….Pages 87-103
Diffusions on a R-Tree without Leaves: Snakes and Spiders….Pages 105-128
R–Trees from Coalescing Particle Systems….Pages 129-141
Subtree Prune and Re-Graft….Pages 143-162
Back Matter….Pages 163-193
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