Buffon needle lands in ϵ-neighborhood of a 1-dimensional Sierpinski Gasket with probability at most

Abstract: In recent years, relatively sharp quantitative results in the spirit of the Besicovitch projection theorem have been obtained for self-similar sets by studying the norms of the “projection multiplicity” functions, , where is the number of connected components of the partial fractal set that orthogonally project in the θ direction to cover x. In Nazarov et al. (2008) , it was shown that n-th partial 4-corner Cantor set with self-similar scaling factor 1/4 decays in Favard length at least as fast as , for . In Bond and Volberg (2009) , this same estimate was proved for the 1-dimensional Sierpinski gasket for some . A few observations were needed to adapt the approach of Nazarov et al. (2008) to the gasket: we sketch them here. We also formulate a result about all self-similar sets of dimension 1. [Copyright &y& Elsevier]