Buffon's needle estimates for rational product Cantor sets

Matthew Bond, Izabella Laba, Alexander Volberg

Let $S_{\infty }=A_{\infty }\times B_{\infty }$ be a self-similar product Cantor set in the complex plane, defined via $S_{\infty }={\bigcup }_{j=1}^L{T}_j(S_{\infty })$, where $T_j:\C\to\C$ have the…