Ordered random walks [article]

Peter Eichelsbacher, Wolfgang Konig
2006 arXiv   pre-print
We construct the conditional version of k independent and identically distributed random walks on 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
more » ... 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.
arXiv:math/0610850v1 fatcat:qkxvmpc4avcjfelz732sgieify