Brownian motion in a Weyl chamber, non-colliding particles, and random matrices

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 35, Issue 2, 1999, Pages 177-204

  Grabiner, David J ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033089822     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0246-0203(99)80010-7     Document Type: Article

References (29)

1. J. F. Adams, Lectures on Lie Groups, University of Chicago Press, 1969.
2. P. Bérard and G. Besson, Spectres et groupes cristallographiques II: Domaines sphériques, Ann. Inst. Fourier, Vol. 30, 3. 1980, pp. 237-248.
3. P. Biane, Minuscule weights and random walks on lattices, Quant. Prob. Rel. Topics, Vol. 7, 1992, pp. 51-65.
4. P. Biane, Permutation model for semi-circular systems and quantum random walks, Pacific J. Math., Vol. 171, 1995, pp. 373-387.
5. N. Bourbaki, Groupes et Algèbres de Lie, Chapters 4, 5, 6. Hermann, Paris, 1968.
6. N. Bourbaki, Groupes et Algèbres de Lie, Chapter 9. Masson, Paris, 1982.
7. D. L. Burkholder, Exit times of Brownian motion, harmonic majorization, and Hardy spaces, Adv. Math., Vol. 26, 1977, pp. 182-205.
8. n of Brownian motion, Prob. Th. Rel. Fields, Vol. 74, 1987, pp. 1-29.
9. J. L. Doob, Classical Potential Theory and its Probabilistic Counterpart, Springer-Verlag, New York, 1984.
10. F. J. Dyson, A Brownian-motion model for the eigenvalues of a random matrix, J. Math. Phys., Vol. 3, 1962, pp. 1191-1198.
11. D. Freedman, Brownian Motion and Diffusion, Holden-Day, San Francisco; second edition published by Springer-Verlag, New York, 1971.
12. I. M. Gessel and D. Zeilberger, Random walk in a Weyl chamber, Proc. Amer. Math. Soc., Vol. 115, 1992, pp. 27-31.
13. D. J. Grabiner and P. Magyar, Random walks in Weyl chambers and the decomposition of tensor powers, J. Alg. Combin., Vol. 2, 1993, pp. 239-260.
14. J. M. Harrison, Brownian Motion and Stochastic Flow Systems, John Wiley and Sons, New York, 1985.
15. J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer-Verlag, New York, 1972.
16. D. Hobson and W. Werner, Non-colliding Brownian motion on the circle. Bull. London. Math. Soc., Vol. 28, 1996, pp. 643-650.
17. S. P. Karlin and G. MacGregor, Coincidence probabilities, Pacific. J. Math., Vol. 9, 1959, pp. 1141-1164.
18. S. P. Karlin and H. M. Taylor, A Second Course in Stochastic Processes, Academic Press, New York, 1981.
19. I. G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford University Press, 1979.
20. I. G. Macdonald, Some conjectures for root systems, SIAM J. Math. Anal., Vol. 13, 1982, pp. 988-1007.
21. H. P. McKean, Stochastic Integrals, Academic Press, New York, 1969.
22. M. L. Mehta, Random Matrices: Second Edition, Academic Press, New York, 1991.
23. N. O'Connell and A. Unwin, Collision times and exit times from cones: A duality, Stock. Proc. Appl., Vol. 43, 1992, pp. 291-301.
24. J. Pitman, One-dimensional Brownian motion and the three-dimensional Bessel process, Ann. Appl. Prob., Vol. 7, 1975, pp. 511-526.
25. R. A. Proctor, Reflection and algorithm proofs of some more Lie group dual pair identities. J. Combin. Th. A, Vol. 62, 1993, pp. 107-127.
26. A. Selberg, Bemerkinger om et multipelt integral, Norsk Mathematisk Tidsskrift, Vol. 26, 1944, pp. 71-78.
27. T. Watanabe and S. G. Mohanty, On an inclusion-exclusion formula based on the reflection principle, Discrete Math, Vol. 64, 1987, pp. 281-288.
28. D. Williams, Path decomposition and continuity of local time for one-dimensional diffusions, Proc. London Math. Soc., Vol. 28, 1974, pp. 738-768.
29. D. Zeilberger, Andre's reflection proof generalized to the many-candidate ballot problem. Discrete Math, Vol. 44, 1983, pp. 325-326.