Branching Random Walks
Shi, Zhan.
Branching Random Walks École d'Été de Probabilités de Saint-Flour XLII – 2012 / [electronic resource] : by Zhan Shi. - 1st ed. 2015. - X, 133 p. 8 illus., 6 illus. in color. online resource. - École d'Été de Probabilités de Saint-Flour, 2151 0721-5363 ; . - École d'Été de Probabilités de Saint-Flour, 2151 .
I Introduction -- II Galton–Watson trees -- III Branching random walks and martingales -- IV The spinal decomposition theorem -- V Applications of the spinal decomposition theorem -- VI Branching random walks with selection -- VII Biased random walks on Galton–Watson trees -- A Sums of i.i.d. random variables -- References.
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. .
9783319253725
10.1007/978-3-319-25372-5 doi
Distribution (Probability theory.
Probability Theory and Stochastic Processes.
QA273.A1-274.9 QA274-274.9
519.2
Branching Random Walks École d'Été de Probabilités de Saint-Flour XLII – 2012 / [electronic resource] : by Zhan Shi. - 1st ed. 2015. - X, 133 p. 8 illus., 6 illus. in color. online resource. - École d'Été de Probabilités de Saint-Flour, 2151 0721-5363 ; . - École d'Été de Probabilités de Saint-Flour, 2151 .
I Introduction -- II Galton–Watson trees -- III Branching random walks and martingales -- IV The spinal decomposition theorem -- V Applications of the spinal decomposition theorem -- VI Branching random walks with selection -- VII Biased random walks on Galton–Watson trees -- A Sums of i.i.d. random variables -- References.
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. .
9783319253725
10.1007/978-3-319-25372-5 doi
Distribution (Probability theory.
Probability Theory and Stochastic Processes.
QA273.A1-274.9 QA274-274.9
519.2