Umfang:
1 Online-Ressource (xii, 226 Seiten)
ISBN:
9781107415690
Serie:
London Mathematical Society lecture note series 438
Inhalt:
This introduction to random walks on infinite graphs gives particular emphasis to graphs with polynomial volume growth. It offers an overview of analytic methods, starting with the connection between random walks and electrical resistance, and then proceeding to study the use of isoperimetric and Poincaré inequalities. The book presents rough isometries and looks at the properties of a graph that are stable under these transformations. Applications include the 'type problem': determining whether a graph is transient or recurrent. The final chapters show how geometric properties of the graph can be used to establish heat kernel bounds, that is, bounds on the transition probabilities of the random walk, and it is proved that Gaussian bounds hold for graphs that are roughly isometric to Euclidean space. Aimed at graduate students in mathematics, the book is also useful for researchers as a reference for results that are hard to find elsewhere.
Anmerkung:
Title from publisher's bibliographic system (viewed on 20 Mar 2017)
Weitere Ausg.:
ISBN 9781107674424
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe Barlow, Martin T., 1953 - Random walks and heat kernels on graphs Cambridge : Cambridge University Press, 2017 ISBN 9781107674424
Sprache:
Englisch
Fachgebiete:
Mathematik
Schlagwort(e):
Irrfahrtsproblem
;
Unendlicher Graph
DOI:
10.1017/9781107415690
Mehr zum Autor:
Barlow, Martin T. 1953-
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