Self-Similar Corrections to the Ergodic Theorem for the Pascal-Adic Transformation
Probability
2007-05-23 v3 Combinatorics
Abstract
Let T be the Pascal-adic transformation. For any measurable function g, we consider the corrections to the ergodic theorem sum_{k=0}^{j-1} g(T^k x) - j/l sum_{k=0}^{l-1} g(T^k x). When seen as graphs of functions defined on {0,...,l-1}, we show for a suitable class of functions g that these quantities, once properly renormalized, converge to (part of) the graph of a self-affine function. The latter only depends on the ergodic component of x, and is a deformation of the so-called Blancmange function. We also briefly describe the links with a series of works on Conway recursive $10,000 sequence.
Cite
@article{arxiv.math/0406078,
title = {Self-Similar Corrections to the Ergodic Theorem for the Pascal-Adic Transformation},
author = {Elise Janvresse and Thierry de la Rue and Yvan Velenik},
journal= {arXiv preprint arXiv:math/0406078},
year = {2007}
}
Comments
version to appear in Stochastics and Dynamics. We added a discussion on the links with Conway 10,000$ recursive sequence