Geometric law for numbers of returns until a hazard under $\varphi$-mixing

Yuri Kifer, Fan Yang

We consider a $\varphi$-mixing shift $T$ on a sequence space $\Omega$ and study the number of returns $\{T^k\omega \in U\}$ to a union $U$ of cylinders of length $n$ until the first return $\{ T^k…