The Power Law for Buffon’s Needle Landing near the Sierpinski Gasket

In this paper we get a power estimate from above of the probability that Buffon’s needle will land within distance 3 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 [14]: we still need the technique of [14] 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.