Interpolation of Random Hyperplanes
Probability
2007-06-13 v1 Statistics Theory
Statistics Theory
Abstract
Let {(Z_i,W_i):i=1,...,n} be uniformly distributed in [0,1]^d * G(k,d), where G(k,d) denotes the space of k-dimensional linear subspaces of R^d. For a differentiable function f from [0,1]^k to [0,1]^d we say that f interpolates (z,w) in [0,1]^d * G(k,d) if there exists x in [0,1]^k such that f(x) = z and vec{f}(x) = w, where vec{f}(x) denotes the tangent space at x defined by f. For a smoothness class F of H\"older type, we obtain probability bounds on the maximum number of points a function f in F interpolates.
Keywords
Cite
@article{arxiv.math/0609340,
title = {Interpolation of Random Hyperplanes},
author = {Ery Arias-Castro},
journal= {arXiv preprint arXiv:math/0609340},
year = {2007}
}