Evans, Steven Neil.
Probability and Real Trees École d'Été de Probabilités de Saint-Flour XXXV - 2005 / [electronic resource] : by Steven Neil Evans. - Berlin, Heidelberg : Springer Berlin Heidelberg, 2008. - XI, 201 p. online resource. - Lecture Notes in Mathematics, 1920 0075-8434 ; . - Lecture Notes in Mathematics, 1920 .
Around the Continuum Random Tree -- R-Trees and 0-Hyperbolic Spaces -- Hausdorff and Gromov–Hausdorff Distance -- Root Growth with Re-Grafting -- The Wild Chain and other Bipartite Chains -- Diffusions on a R-Tree without Leaves: Snakes and Spiders -- R–Trees from Coalescing Particle Systems -- Subtree Prune and Re-Graft.
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.
9783540747987
10.1007/978-3-540-74798-7 doi
Mathematics.
Combinatorics.
Geometry.
Distribution (Probability theory).
Mathematics.
Probability Theory and Stochastic Processes.
Combinatorics.
Geometry.
QA273.A1-274.9 QA274-274.9
519.2
Probability and Real Trees École d'Été de Probabilités de Saint-Flour XXXV - 2005 / [electronic resource] : by Steven Neil Evans. - Berlin, Heidelberg : Springer Berlin Heidelberg, 2008. - XI, 201 p. online resource. - Lecture Notes in Mathematics, 1920 0075-8434 ; . - Lecture Notes in Mathematics, 1920 .
Around the Continuum Random Tree -- R-Trees and 0-Hyperbolic Spaces -- Hausdorff and Gromov–Hausdorff Distance -- Root Growth with Re-Grafting -- The Wild Chain and other Bipartite Chains -- Diffusions on a R-Tree without Leaves: Snakes and Spiders -- R–Trees from Coalescing Particle Systems -- Subtree Prune and Re-Graft.
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.
9783540747987
10.1007/978-3-540-74798-7 doi
Mathematics.
Combinatorics.
Geometry.
Distribution (Probability theory).
Mathematics.
Probability Theory and Stochastic Processes.
Combinatorics.
Geometry.
QA273.A1-274.9 QA274-274.9
519.2