A distributional limit law for the continued fraction digit sum

✍ Scribed by Marc Kesseböhmer; Mehdi Slassi

• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 186 KB
• Volume: 281
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200510679

✦ Synopsis

Abstract

We consider the continued fraction digits as random variables measured with respect to Lebesgue measure. The logarithmically scaled and normalised fluctuation process of the digit sums converges strongly distributional to a random variable uniformly distributed on the unit interval. For this process normalised linearly we determine a large deviation asymptotic. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)