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Interpolation Percolation

   
@article{EJP895,
	author = {Martin Zerner},
	title = {Interpolation Percolation},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {16},
	year = {2011},
	keywords = {Interpolation, path connected, percolation, stationary random set.},
	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.},
	pages = {no. 33, 981-1000},
	issn = {1083-6489},
	doi = {10.1214/EJP.v16-895},    
        url = {http://ejp.ejpecp.org/article/view/895}}