A natural probability measure derived from Stern's diatomic sequence
Number Theory
2018-03-19 v2
Abstract
Stern's diatomic sequence with its intrinsic repetition and refinement structure between consecutive powers of gives rise to a rather natural probability measure on the unit interval. We construct this measure and show that it is purely singular continuous, with a strictly increasing, H\"older continuous distribution function. Moreover, we relate this function with the solution of the dilation equation for Stern's diatomic sequence.
Cite
@article{arxiv.1706.00187,
title = {A natural probability measure derived from Stern's diatomic sequence},
author = {Michael Baake and Michael Coons},
journal= {arXiv preprint arXiv:1706.00187},
year = {2018}
}
Comments
13 pages, 3 figures; minor revision with some improvements and updates