WIAS Preprint No. 1533, (2010)

Brownian motion in a truncated Weyl chamber



Authors

  • König, Wolfgang
  • Schmid, Patrick

2010 Mathematics Subject Classification

  • 60J65 60F10

Keywords

  • Weyl chamber, non-colliding Brownian motions, Karlin-McGregor formula, non-colliding probability, non-exit probability, eigenvalue expansion, réduite

Abstract

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.

Appeared in

  • Markov Process. Related Fields, 17 (2011) pp. 499--522.

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