@article{EJP539,
author = {Peter Eichelsbacher and Wolfgang König},
title = {Ordered Random Walks},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {13},
year = {2008},
keywords = {Dyson's Brownian motions; Vandermonde determinant; Doob h-transform; non-colliding random walks; non-intersecting random processes; fluctuation theory.},
abstract = {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.},
pages = {no. 46, 1307-1336},
issn = {1083-6489},
doi = {10.1214/EJP.v13-539},
url = {http://ejp.ejpecp.org/article/view/539}}