Branching random walks : École d'Été de Probabilités de Saint-Flour XLII -- 2012 / Zhan Shi.Material type: TextSeries: Lecture notes in mathematics (Springer-Verlag): 2151.Publisher: Cham : Springer, 2015Description: 1 online resource (x, 133 pages) : illustrations (some color)Content type: text Media type: computer Carrier type: online resourceISBN: 9783319253725; 3319253727; 3319253719; 9783319253718Subject(s): Random walks (Mathematics) -- Congresses | Branching processes -- Congresses | Mathematics -- Probability & Statistics -- General | Probability & statistics | Branching processes | Random walks (Mathematics)Genre/Form: Electronic books. | Conference papers and proceedings. Additional physical formats: Printed edition:: No titleDDC classification: 519.2/82 LOC classification: QA274.73Online resources: Click here to access online
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Includes bibliographical references.
Online resource; title from PDF title page (SpringerLink, viewed February 16, 2016).
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.