A distributional limit law for the continued fraction digit sum

Abstract

We consider the continued fraction digits as random variables measured with respect to Lebesgue measure. The logarithmically scaled and normalized fluctuation process of the digit sums converges strongly distributional to a random variable uniformly distributed on the unit interval. For this process normalized linearly we determine a large deviation asymptotic.

14 pages, 1 figure

References in corpus (3)

• Critical waiting time processes in infinite ergodic theory
• Limit laws for distorted return time processes for infinite measure preserving transformations
• Large deviation asymptotics for continued fraction expansions

Cited by in corpus (5)

• On the Lebesgue measure of sum-level sets for continued fractions
• On the asymptotics of the $\alpha$-Farey transfer operator
• A dichotomy between uniform distributions of the Stern-Brocot and the Farey sequence
• A remark on the extreme value theory for continued fractions
• On the convergence to equilibrium of unbounded observables under a family of intermittent interval maps