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Random walks conditioned to stay in Weyl chambers of type C and D · Around

2009

Random walks conditioned to stay in Weyl chambers of type C and D

Koenig, Wolfgang, Schmid, Patrick

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We construct the conditional versions of a multidimensional random walk given that it does not leave the Weyl chambers of type C and of type D, respectively, in terms of a Doob h-transform.

Furthermore, we prove functional limit theorems for the rescaled random walks.
This is an extension of recent work by Eichelsbacher and Koenig who studied the analogous conditioning for the Weyl chamber of type A.
Our proof follows recent work by Denisov and Wachtel who used martingale properties and a strong approximation of random walks by Brownian motion.

Built on

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Karlin, S.P · 1959
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A Brownian-motion model for the eigenvalues of a random matrix,
Dyson, F.J · 1962
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The approximation of partial sums of rv’s,
Major, P · 1976
Earlier work this paper cites.
Classical potential theory and its probabilistic counterpart,
Doob, J.L · 1984
Earlier work this paper cites.
On conditioning a random walk to stay nonnegative,
Bertoin, J · 1994
Earlier work this paper cites.

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