English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we prove an extreme value law for a stochastic process obtainedby iterating the R\'enyi map $x \mapsto \beta x \pmod 1$, where we assume that$\beta>1$ is an integer. Haiman (2018) derived a recursion formula for theLebesgue measure of threshold exceedance sets. We show how this recursionformula is related to a rescaled version of the $k$-generalized Fibonaccisequence. For the latter sequence we derive a Binet formula which leads to aclosed-form expression for the distribution of partial maxima of the stochasticprocess. The proof of the extreme value law is completed by deriving sharpbounds for the dominant root of the characteristic polynomial associated withthe Fibonacci sequence.

Generalized Fibonacci numbers and extreme value laws for the R\'enyi map