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 almost sure 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.
Citation
Martin Zerner. "Interpolation Percolation." Electron. J. Probab. 16 981 - 1000, 2011. https://doi.org/10.1214/EJP.v16-895
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