Electronic Journal of Probability

Interpolation Percolation

Martin Zerner

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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.

Article information

Electron. J. Probab., Volume 16 (2011), paper no. 33, 981-1000.

Accepted: 23 May 2011
First available in Project Euclid: 1 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 60K35.
Secondary: 54D05: Connected and locally connected spaces (general aspects)

Interpolation path connected percolation stationary random set

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Zerner, Martin. Interpolation Percolation. Electron. J. Probab. 16 (2011), paper no. 33, 981--1000. doi:10.1214/EJP.v16-895. https://projecteuclid.org/euclid.ejp/1464820202

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