Buffon needles landing near Sierpinski gasket

Abstract

In this paper we modify the method of Nazarov, Peres, and Volberg "The power law for the Buffon needle probability of the four-corner Cantor set", arXiv:0801.2942, to get an estimate from above of the Buffon needle probability of the $n$--th partially constructed Sierpinski gasket of Hausdorff dimension 1.