Buffon's needle estimates for rational product Cantor sets

Details Buffon's needle estimates for rational product Cantor sets Buffon's needle estimates for rational product Cantor sets

2011-09-05

arxiv.org/abs/1109.1031v3

Mathematics

Classical Analysis and ODEs

39 pages. Minor corrections and clarifications. Hopefully this time the replacement will work

Scientific paper

In this paper, we investigate the probability that "Buffon's Needle" lands near a one-dimensional self-similar product set in the complex plane, where the similarity maps have rational centers and identical scalings. If the factors $A$ and $B$ are defined by at most 6 similarities, then the likelihood that the needle intersects an $e^{-n}$-neighborhood of such a set is at most $Cn^{-p/\log\log n}$ for some $p>0$.

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