EAN: 9783642213984

HARMONIC FUNCTIONS AND POTENTIALS ON FINITE OR ...

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.

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