Probabilistic embedding of discrete sets as continuous metric spaces

Ph Blanchard; D. Volchenkov

doi:10.1080/17442500902917326

Probabilistic embedding of discrete sets as continuous metric spaces

Ph Blanchard, D. Volchenkov

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Any symmetric affinity function w: V × V → ℝ₊ 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.

Original language	English
Pages (from-to)	259-268
Number of pages	10
Journal	Stochastics
Volume	81
Issue number	3-4
DOIs	https://doi.org/10.1080/17442500902917326
State	Published - 2009

Keywords

Euclidean space
Probabilistic analogue
Random walk

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title = "Probabilistic embedding of discrete sets as continuous metric spaces",

abstract = "Any symmetric affinity function w: V × V → ℝ+ 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.",

keywords = "Euclidean space, Probabilistic analogue, Random walk",

author = "Ph Blanchard and D. Volchenkov",

note = "Funding Information: This work has been supported by the Volkswagen Foundation (Germany) in the framework of the project {\textquoteleft}Network formation rules, random set graphs and generalized epidemic processes{\textquoteright} (Contract no Az.: I/82 418).",

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KW - Probabilistic analogue

KW - Random walk

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Probabilistic embedding of discrete sets as continuous metric spaces

Abstract

Keywords

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