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Mathematics - Probability Theory and Stochastic Processes | Potential Theory on Infinite Networks

Potential Theory on Infinite Networks

Series: Lecture Notes in Mathematics, Vol. 1590

Soardi, Paolo M.

1994, VIII, 196 p.

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  • About this book

The aim of the book is to give a unified approach to new developments in discrete potential theory and infinite network theory. The author confines himself to the finite energy case, but this does not result in loss of complexity. On the contrary, the functional analytic machinery may be used in analogy with potential theory on Riemann manifolds.
The book is intended for researchers with interdisciplinary interests in one of the following fields: Markov chains, combinatorial graph theory, network theory, Dirichlet spaces, potential theory, abstract harmonic analysis, theory of boundaries.

Content Level » Research

Keywords » Infinite Networks - Markov chain - Potential theory - boundary - dirichlet - discrete potential networks - graph theory - harmonic analysis

Related subjects » Analysis - Probability Theory and Stochastic Processes

Table of contents 

Kirchhoff's laws.- Finite networks.- Currents and potentials withfinite energy.- Uniqueness and related topics.- Some examples and computations.- Royden's compactification.- Rough isometries.

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