The Power Law For Buffon's Needle Landing Near the Sierpinski Gasket

Details The Power Law For Buffon's Needle Landing Near the Sierpinski Gasket The Power Law For Buffon's Needle Landing Near the Sierpinski Gasket

2009-11-02

arxiv.org/abs/0911.0233v2

Mathematics

Classical Analysis and ODEs

35 pages

Scientific paper

In this paper we get a power estimate from above of the probability that Buffon's needle will land within distance 3^{-n} of Sierpinski's gasket of Hausdorff dimension 1. In comparison with the case of 1/4 corner Cantor set considered in Nazarov, Peres, and the second author: we still need the technique of arXiv:0801.2942 for splitting the directions to good and bad ones, but the case of Sierpinski gasket is considerably more generic and lacks symmetry, resulting in a need for much more careful estimates of zeros of the Fourier transform of Cantor measure.

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