Rank Independence and Rearrangements of Random Variables
| dc.creator | Gnedin, Alexander | |
| dc.creator | Nitecki, Zbigniew | |
| dc.date | 2005-05-31 | |
| dc.date.accessioned | 2026-07-07T05:20:25Z | |
| dc.date.available | 2026-07-07T05:20:25Z | |
| dc.description | A rearrangement of $n$ independent uniform $[0,1]$ random variables is a sequence of $n$ random variables $Y_1,...,Y_n$ whose vector of order statistics has the same distribution as that for the $n$ uniforms. We consider rearrangements satisfying the strong rank independence condition, that the rank of $Y_k$ among $Y_1,...,Y_k$ is independent of the values of $Y_1,...,Y_{k-1}$, for $k=1,...,n$. Nontrivial examples of such rearrangements are the travellers' processes defined by Gnedin and Krengel. We show that these are the only examples when $n=2$, and when certain restrictive assumptions hold for $n\geq 3$; we also construct a new class of examples of such rearrangements for which the restrictive assumptions do not hold. | |
| dc.description | 29 pages | |
| dc.identifier | https://arxiv.org/abs/math/0505692 | |
| dc.identifier | http://arxiv.org/abs/math/0505692 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75371 | |
| dc.subject | Probability | |
| dc.subject | 60C05; 62G30 | |
| dc.title | Rank Independence and Rearrangements of Random Variables | |
| dc.type | text |