Probabilistic Embedding Of Discrete Sets As Continuous Metric Spaces

Ph. Blanchard; D. Volchenkov

Probabilistic Embedding Of Discrete Sets As Continuous Metric Spaces

Mathematical Physics 2008-04-29 v1 math.MP

Authors: Ph. Blanchard , D. Volchenkov

Abstract

Any symmetric affinity function $w: V\times V \to \mathbb{R}_+$ 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 2-dimensional lattice.

Keywords

isometric embedding positive maps in quantum information mathematical physics

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@article{arxiv.0804.4434,
  title  = {Probabilistic Embedding Of Discrete Sets As Continuous Metric Spaces},
  author = {Ph. Blanchard and D. Volchenkov},
  journal= {arXiv preprint arXiv:0804.4434},
  year   = {2008}
}

Comments

13 pages, 7 figures, conference "Stochastic Analysis and Applications", 5-10 November 2007 Hammamet, Tunis

Probabilistic Embedding Of Discrete Sets As Continuous Metric Spaces

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