Self-Similar Corrections to the Ergodic Theorem for the Pascal-Adic Transformation
| dc.creator | Janvresse, Elise | |
| dc.creator | de la Rue, Thierry | |
| dc.creator | Velenik, Yvan | |
| dc.date | 2004-06-04 | |
| dc.date | 2005-02-23 | |
| dc.date.accessioned | 2026-07-07T05:08:52Z | |
| dc.date.available | 2026-07-07T05:08:52Z | |
| dc.description | 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 $10,000 sequence. | |
| dc.description | version to appear in Stochastics and Dynamics. We added a discussion on the links with Conway 10,000$ recursive sequence | |
| dc.identifier | https://arxiv.org/abs/math/0406078 | |
| dc.identifier | http://arxiv.org/abs/math/0406078 | |
| dc.identifier | Stochastics and dynamics 5, no.1, pp 1-25 (2005) | |
| dc.identifier | doi:10.1142/S0219493705001250 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71435 | |
| dc.subject | Probability | |
| dc.subject | Combinatorics | |
| dc.subject | 37A30; 28A80 | |
| dc.title | Self-Similar Corrections to the Ergodic Theorem for the Pascal-Adic Transformation | |
| dc.type | text |