Ordered random walks
| dc.creator | Eichelsbacher, Peter | |
| dc.creator | Konig, Wolfgang | |
| dc.date | 2006-10-27 | |
| dc.date.accessioned | 2026-07-07T07:29:32Z | |
| dc.date.available | 2026-07-07T07:29:32Z | |
| dc.description | We construct the conditional version of $k$ independent and identically distributed random walks on $\R$ given that they stay in strict order at all times. This is a generalisation of so-called non-colliding or non-intersecting random walks, the discrete variant of Dyson's Brownian motions, which have been considered yet only for nearest-neighbor walks on the lattice. Our only assumptions are moment conditions on the steps and the validity of the local central limit theorem. The conditional process is constructed as a Doob $h$-transform with some positive regular function $V$ that is strongly related with the Vandermonde determinant and reduces to that function for simple random walk. Furthermore, we prove an invariance principle, i.e., a functional limit theorem towards Dyson's Brownian motions, the continuous analogue. | |
| dc.description | 26 pages | |
| dc.identifier | https://arxiv.org/abs/math/0610850 | |
| dc.identifier | http://arxiv.org/abs/math/0610850 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/118146 | |
| dc.subject | Probability | |
| dc.subject | 60G50, 60F17 | |
| dc.title | Ordered random walks | |
| dc.type | text |