Uniformly Discrete Forests with Poor Visibility. (9th October 2017)

• Record Type: Journal Article
• Authors: ALON, NOGA
• Is Part Of: Combinatorics, probability and computing. Volume 27:Number 4(2018)
• Page Start: 442
• Page End: 448
• Publication Date: 2017-10-09
• Subjects: Primary 51F99, -- Secondary 52C99; Combinatorial analysis -- Periodicals; Probabilities -- Periodicals; Computer science -- Mathematics -- Periodicals; 511.6
• DOI: 10.1017/S0963548317000505
• Languages: English
• ISSNs: 0963-5483

Abstract

Abstract : 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.