Conditional limit theorems for ordered random walks

Details Conditional limit theorems for ordered random walks Conditional limit theorems for ordered random walks

2009-07-16

arxiv.org/abs/0907.2854v1

Mathematics

Probability

26 pages

Scientific paper

In a recent paper of Eichelsbacher and Koenig (2008) the model of ordered random walks has been considered. There it has been shown that, under certain moment conditions, one can construct a k-dimensional random walk conditioned to stay in a strict order at all times. Moreover, they have shown that the rescaled random walk converges to the Dyson Brownian motion. In the present paper we find the optimal moment assumptions for the construction of the conditional random walk and generalise the limit theorem for this conditional process.

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