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Mathematics - Probability Theory and Stochastic Processes | Probability and Real Trees - École d'Été de Probabilités de Saint-Flour XXXV-2005

Probability and Real Trees

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

Evans, Steven N.

2008, XI, 201 p.

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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.

Content Level » Research

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

Related subjects » Geometry & Topology - Probability Theory and Stochastic Processes

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