Interpolation percolation

Details Interpolation percolation Interpolation percolation

2010-07-29

arxiv.org/abs/1007.5327v2

Mathematics

Probability

Now 21 pages, 8 figures. Added some references, Remark 4 and Examples 4 and 6; removed the former Open Problem 6

Scientific paper

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.

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