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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 81, 2009 - Issue 3-4: Stochastic Analysis
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Original Articles

Probabilistic embedding of discrete sets as continuous metric spaces

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Pages 259-268 | Received 28 Apr 2008, Accepted 11 Aug 2008, Published online: 23 Jul 2009
 

Abstract

Any symmetric affinity function defined on a discrete set V induces Euclidean space structure on V. In particular, an undirected graph specified by an affinity (or adjacency) matrix can be considered as a metric topological space. We have calculated the visual representations of the probabilistic locus for a chain, a polyhedron and a finite 2D lattice.

Acknowledgements

This work has been supported by the Volkswagen Foundation (Germany) in the framework of the project ‘Network formation rules, random set graphs and generalized epidemic processes’ (Contract no Az.: I/82 418).

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