منابع مشابه
Percolation and Minimal Spanning Trees
Consider a random set V n of points in the box n; n) d , generated either by a Poisson process with density p or by a site percolation process with parameter p. We analyse the empirical distribution function F n of the lengths of edges in a minimal (Euclidean) spanning tree T n on V n. We express the limit of F n , as n ! 1, in terms of the free energies of a family of percolation processes der...
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In the manifold learning problem one seeks to discover a smooth low dimensional surface, i.e., a manifold embedded in a higher dimensional linear vector space, based on a set of measured sample points on the surface. In this paper we consider the closely related problem of estimating the manifold’s intrinsic dimension and the intrinsic entropy of the sample points. Specifically, we view the sam...
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We model the distribution of normalized interpoint distances (IDs) on the minimal spanning tree (MST) using multivariate beta vectors. We define overlapping sums of the components of a Dirichlet distribution to construct multivariate beta distributions. We also use a multivariate normal copula with beta marginals to define beta vectors. Based on the ordered IDs of the MST, we define a multivari...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2003
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-03-07182-x