Electronic Journal of Probability

Interpolation Percolation

Martin Zerner

Full-text: Open access

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464820202

Digital Object Identifier
doi:10.1214/EJP.v16-895

Mathematical Reviews number (MathSciNet)
MR2801458

Zentralblatt MATH identifier
1225.60155

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

Keywords
Interpolation path connected percolation stationary random set

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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