Potential Theory on Infinite Networks
Soardi, Paolo M.
Potential Theory on Infinite Networks [electronic resource] / by Paolo M. Soardi. - VIII, 196 p. online resource. - Lecture Notes in Mathematics, 1590 0075-8434 ; . - Lecture Notes in Mathematics, 1590 .
Kirchhoff's laws -- Finite networks -- Currents and potentials withfinite energy -- Uniqueness and related topics -- Some examples and computations -- Royden's compactification -- Rough isometries.
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.
9783540487982
10.1007/BFb0073995 doi
Distribution (Probability theory.
Combinatorics.
Potential theory (Mathematics).
Probability Theory and Stochastic Processes.
Combinatorics.
Potential Theory.
QA273.A1-274.9 QA274-274.9
519.2
Potential Theory on Infinite Networks [electronic resource] / by Paolo M. Soardi. - VIII, 196 p. online resource. - Lecture Notes in Mathematics, 1590 0075-8434 ; . - Lecture Notes in Mathematics, 1590 .
Kirchhoff's laws -- Finite networks -- Currents and potentials withfinite energy -- Uniqueness and related topics -- Some examples and computations -- Royden's compactification -- Rough isometries.
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.
9783540487982
10.1007/BFb0073995 doi
Distribution (Probability theory.
Combinatorics.
Potential theory (Mathematics).
Probability Theory and Stochastic Processes.
Combinatorics.
Potential Theory.
QA273.A1-274.9 QA274-274.9
519.2