Interpolation percolation
Probability
2011-05-17 v2
Abstract
Let X be a countably infinite set of real numbers and let Y_x, x \in X, be an independent family of stationary random subsets of the real numbers, e.g. homogeneous Poisson point processes. We give criteria for the a.s. existence of various "regular" functions f with the property that f(x) \in Y_x for all x \in X. Several open questions are posed.
Cite
@article{arxiv.1007.5327,
title = {Interpolation percolation},
author = {Martin P. W. Zerner},
journal= {arXiv preprint arXiv:1007.5327},
year = {2011}
}
Comments
Now 21 pages, 8 figures. Added some references, Remark 4 and Examples 4 and 6; removed the former Open Problem 6