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Uniformly Discrete Forests with Poor Visibility

Part of: Metric geometry Discrete geometry

Published online by Cambridge University Press:  09 October 2017

NOGA ALON
NOGA ALON*
Affiliation:
Sackler School of Mathematics and Blavatnik School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA (e-mail: nogaa@tau.ac.il)
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Abstract

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We prove that there is a set F in the plane so that the distance between any two points of F is at least 1, and for any positive ϵ < 1, and every line segment in the plane of length at least ϵ−1−o(1), there is a point of F within distance ϵ of the segment. This is tight up to the o(1)-term in the exponent, improving earlier estimates of Peres, of Solomon and Weiss, and of Adiceam.

MSC classification

Primary: 51F99: None of the above, but in this section
Secondary: 52C99: None of the above, but in this section
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 27 , Special Issue 4: Special Issue: Oberwolfach Workshop , July 2018 , pp. 442 - 448
Copyright
Copyright © Cambridge University Press 2017 

References

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