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Harmonic Functions and Potentials on Finite or Infinite Networks
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) pote...
| Call Number: | Libro Electrónico |
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| Main Author: | |
| Corporate Author: | |
| Format: | Electronic eBook |
| Language: | Inglés |
| Published: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2011.
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| Edition: | 1st ed. 2011. |
| Series: | Lecture Notes of the Unione Matematica Italiana,
12 |
| Subjects: | |
| Online Access: | Texto Completo |
| Summary: | 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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| Physical Description: | X, 141 p. online resource. |
| ISBN: | 9783642213991 |
| ISSN: | 1862-9121 ; |