On the Stochastic Rank of Metric Functions

Details On the Stochastic Rank of Metric Functions On the Stochastic Rank of Metric Functions

2008-10-30

arxiv.org/abs/0810.5549v3

Mathematics

Metric Geometry

23 pages, 1 table

Scientific paper

For a class of integral operators with kernels metric functions on manifold we find some necessary and sufficient conditions to have finite rank. The problem we pose has a stochastic nature and boils down to the following alternative question. For a random sample of discrete points, what will be the probability the symmetric matrix of pairwise distances to have full rank? When the metric is an analytic function, the question finds full and satisfactory answer. As an important application, we consider a class of tensor systems of equations formulating the problem of recovering a manifold distribution from its covariance field and solve this problem for representing manifolds such as Euclidean space and unit sphere.

Affiliated with

Also associated with

No associations

Rating

On the Stochastic Rank of Metric Functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Stochastic Rank of Metric Functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Stochastic Rank of Metric Functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-279213