The power law for the Buffon needle probability of the four-corner Cantor set

Fedor Nazarov, Yuval Peres, Alexander Volberg

Let $C_n$ be the $n$-th generation in the construction of the middle-half Cantor set. The Cartesian square $K_n$ of $C_n$ consists of $4^n$ squares of side-length $4^{-n}$. The cha…