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Ordered random walks
[article]
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
arXiv:math/0610850v1
fatcat:qkxvmpc4avcjfelz732sgieify