Brownian motion in a truncated Weyl chamber

Details Brownian motion in a truncated Weyl chamber Brownian motion in a truncated Weyl chamber

2010-08-18

arxiv.org/abs/1008.3142v1

Mathematics

Probability

Scientific paper

We examine the non-exit probability of a multidimensional Brownian motion from a growing truncated Weyl chamber. Different regimes are identified according to the growth speed, ranging from polynomial decay over stretched-exponential to exponential decay. Furthermore we derive associated large deviation principles for the empirical measure of the properly rescaled and transformed Brownian motion as the dimension grows to infinity. Our main tool is an explicit eigenvalue expansion for the transition probabilities before exiting the truncated Weyl chamber.

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