Generalized Fibonacci numbers and extreme value laws for the Rényi map

N. B-S. Boer, A. E. Sterk

In this paper we prove an extreme value law for a stochastic process obtained by iterating the Rényi map $x\mapsto \beta x(\mathrm{mod}1)$, where we assume that $\beta >1$ is an integer. Haiman (2…