Harmonic Functions and Potentials on Finite or Infinite Networks

By Victor Anandam

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.

• Format: Paperback
• Language: English
• ISBN: 3642213987
• ISBN13: 9783642213984
• Release Date: June 2011
• Publisher: Springer
• Length: 141 Pages
• Weight: 0.50 lbs.
• Dimensions: 0.4" x 6.1" x 8.9"