Lecture Notes of the Unione Matematica Italiana

Anandam, Victor

Random walks, Markov chains and electrical networks serve as an introduction to the study of real-valued functions on finite or infinite graphs, with appropriate interpretations using probability theory and current-voltage laws. The relation between this type of function theory and the (Newton) potential theory on the Euclidean spaces is well-established. The latter theory has been variously generalized, one example being the axiomatic potential theory on locally compact spaces developed by Brelot, with later ramifications from Bauer, Constantinescu and Cornea. A network is a graph with edge-weights that need not be symmetric. This book presents an autonomous theory of harmonic functions and potentials defined on a finite or infinite network, on the lines of axiomatic potential theory. Random walks and electrical networks are important sources for the advancement of the theory.

Details

Published by: Springer

Publication Date: 2011-06-29

Format: Paperback

ISBN-13: 9783642213984

DOI: 10.1007/978-3-642-21399-1

Dimensions: 235cm x155cm

Pages: 141