A Khinchin Sequence

Kahane-Khinchin type Averages

We prove a Kahane-Khinchin type result with a few random vectors, which are distributed independently with respect to an arbitrary log-concave probability measure on Rn. This is an application of small ball estimate and Chernoff’s method, that has been recently used in the context of Asymptotic Geometric Analysis in [1], [2].

Khinchin theorem and anomalous diffusion.

A recent Letter [M. H. Lee, Phys. Rev. Lett. 98, 190601 (2007)] has called attention to the fact that irreversibility is a broader concept than ergodicity, and that therefore the Khinchin theorem [A. I. Khinchin, (Dover, New York, 1949)] may fail in some systems. In this Letter we show that for all ranges of normal and anomalous diffusion described by a generalized Langevin equation the Khinchi...

Intermediate Convergents and a Metric Theorem of Khinchin

Abstract. A landmark theorem in the metric theory of continued fractions begins this way: Select a non-negative real function f defined on the positive integers and a real number x, and form the partial sums sn of f evaluated at the partial quotients a1, . . . , an in the continued fraction expansion for x. Does the sequence {sn/n} have a limit as n → ∞? In 1935 A. Y. Khinchin proved that the a...

Aging and nonergodicity beyond the Khinchin theorem.

The Khinchin theorem provides the condition that a stationary process is ergodic, in terms of the behavior of the corresponding correlation function. Many physical systems are governed by nonstationary processes in which correlation functions exhibit aging. We classify the ergodic behavior of such systems and suggest a possible generalization of Khinchin's theorem. Our work also quantifies devi...

A generalization of Cauchy-Khinchin-van Dam inequality