The law of series
| dc.creator | Downarowicz, Tomasz | |
| dc.creator | Lacroix, Yves | |
| dc.date | 2006-01-09 | |
| dc.date.accessioned | 2026-07-07T06:58:38Z | |
| dc.date.available | 2026-07-07T06:58:38Z | |
| dc.description | We prove a general ergodic-theoretic result concerning the return time statistic, which, properly understood, sheds some new light on the common sense phenomenon known as {\it the law of series}. Let \proc be an ergodic process on finitely many states, with positive entropy. We show that the distribution function of the normalized waiting time for the first visit to a small cylinder set $B$ is, for majority of such cylinders and up to epsilon, dominated by the exponential distribution function $1-e^{-t}$. This fact has the following interpretation: The occurrences of such a "rare event" $B$ can deviate from purely random in only one direction -- so that for any length of an "observation period" of time, the first occurrence of $B$ "attracts" its further repetitions in this period. | |
| dc.identifier | https://arxiv.org/abs/math/0601166 | |
| dc.identifier | http://arxiv.org/abs/math/0601166 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107439 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37A50, 37A35, 37A05, 60G10 | |
| dc.title | The law of series | |
| dc.type | text |