A strong Liouville theorem for -harmonic functions on graphs.
Holopainen, Ilkka, Soardi, Paolo M. (1997)
Annales Academiae Scientiarum Fennicae. Mathematica
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Holopainen, Ilkka, Soardi, Paolo M. (1997)
Annales Academiae Scientiarum Fennicae. Mathematica
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Commentationes Mathematicae Universitatis Carolinae
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This note attempts to understand graph limits as defined by Lovasz and Szegedy in terms of harmonic analysis on semigroups. This is done by representing probability distributions of random exchangeable graphs as mixtures of characters on the semigroup of unlabeled graphs with node-disjoint union, thereby providing an alternative derivation of de Finetti's theorem for random exchangeable graphs.
Fountoulakis, Nikolaos, McDiarmid, Colin (2002)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Jan Kratochvíl (1988)
Commentationes Mathematicae Universitatis Carolinae
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Subramanian, C.R. (2001)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Publications de l'Institut Mathématique
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CONTENTS1. Introduction...........................................................................5 1.1. Purpose and scope..........................................................5 1.2. Probability-theoretic preliminaries....................................6 1.3. Graphs............................................................................11 1.4. Random graphs..............................................................132. Vertex-degrees....................................................................15 2.1....