Power estimate for Buffon’s needle landing near the Sierpinski gasket

November 2, 2009

Our new, improved paper is online now. Not only is the estimate much sharper thanks to one nice little lemma using Hardy space theory and another using something we call “analytic tiling”*, but you may even be able to read this one.

A 3^{-n}-neighborhood of a 1-dimensional Sierpinski gasket decays in Buffon needle probability at least as fast as C/{n^p}.

* – “Analytic tiling” is essentially our fancy name for the observation that if three unit complex numbers sum to 0, they form an equilateral triangle, and therefore, their third powers sum to a number of size 3. The name is motivated by the role tiling played in Laba and Zhai’s paper on product Cantor sets.


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