Interpolation Percolation

Martin P.W. Zerner (University of Tuebingen)


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.

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Pages: 981-1000

Publication Date: May 23, 2011

DOI: 10.1214/EJP.v16-895


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