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

 Access to full text

 Full (PDF)

1. [1] J.F. Adams, Lectures on Lie Groups, University of Chicago Press, 1969. Zbl0206.31604MR252560
2. [2] P. Bérard and G. Besson, Spectres et groupes cristallographiques II: domaines sphériques, Ann. Inst. Fourier, Vol. 30, 3, 1980, pp. 237-248.. Zbl0426.35073MR597025
3. [3] P. Biane, Minuscule weights and random walks on lattices, Quant. Prob. Rel. Topics, Vol. 7, 1992, pp. 51-65. Zbl0787.60089MR1186654
4. [4] P. Biane, Permutation model for semi-circular systems and quantum random walks, Pacific J. Math., Vol. 171, 1995, pp. 373-387. Zbl0854.60070MR1372234
5. [5] N. Bourbaki, Groupes et Algèbres de Lie, Chapters 4, 5, 6. Hermann, Paris, 1968. Zbl0483.22001MR240238
6. [6] N. Bourbaki, Groupes et Algèbres de Lie, Chapter 9. Masson, Paris, 1982. Zbl0505.22006
7. [7] D.L. Burkholder, Exit times of Brownian motion, harmonic majorization, and Hardy spaces, Adv. Math., Vol. 26, 1977, pp. 182-205. Zbl0372.60112MR474525
8. [8] R.D. Deblassie, Exit times from cones in Rn of Brownian motion, Prob. Th. Rel. Fields, Vol. 74, 1987, pp. 1-29. Zbl0586.60077MR863716
9. [9] J.L. Doob, Classical Potential Theory and its Probabilistic Counterpart, Springer-Verlag, New York, 1984. Zbl0549.31001MR731258
10. [10] F.J. Dyson, A Brownian-motion model for the eigenvalues of a random matrix, J. Math. Phys., Vol. 3, 1962, pp. 1191-1198. Zbl0111.32703MR148397
11. [11] D. Freedman, Brownian Motion and Diffusion, Holden-Day, San Francisco; second edition published by Springer-Verlag, New York, 1971. Zbl0231.60072MR686607
12. [12] I.M. Gessel and D. Zeilberger, Random walk in a Weyl chamber, Proc. Amer. Math. Soc., Vol. 115, 1992, pp. 27-31. Zbl0792.05148MR1092920
13. [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. Zbl0780.60069MR1235279
14. [14] J.M. Harrison, Brownian Motion and Stochastic Flow Systems, John Wiley and Sons, New York, 1985. Zbl0659.60112MR798279
15. [15] J.E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer-Verlag, New York, 1972. Zbl0254.17004MR323842
16. [16] D. Hobson and W. Werner, Non-colliding Brownian motion on the circle, Bull. London. Math. Soc., Vol. 28, 1996, pp. 643-650. Zbl0853.60060MR1405497
17. [17] S.P. Karlin and G. Macgregor, Coincidence probabilities, Pacific. J. Math., Vol. 9, 1959, pp. 1141-1164. Zbl0092.34503MR114248
18. [18] S.P. Karlin and H.M. Taylor, A Second Course in Stochastic Processes, Academic Press, New York, 1981. Zbl0469.60001MR611513
19. [19] I.G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford University Press, 1979. Zbl0487.20007MR553598
20. [20] I.G. Macdonald, Some conjectures for root systems, SIAM J. Math. Anal., Vol. 13, 1982, pp. 988-1007. Zbl0498.17006MR674768
21. [21] H.P. Mckean, Stochastic Integrals, Academic Press, New York, 1969. Zbl0191.46603MR247684
22. [22] M.L. Mehta, Random Matrices: Second Edition, Academic Press, New York, 1991. Zbl0780.60014MR1083764
23. [23] N. O'Connell and A. Unwin, Collision times and exit times from cones: A duality, Stoch. Proc. Appl., Vol. 43, 1992, pp. 291-301. Zbl0765.60083MR1191152
24. [24] J. Pitman, One-dimensional Brownian motion and the three-dimensional Bessel process, Ann. Appl. Prob., Vol. 7, 1975, pp. 511-526. Zbl0332.60055MR375485
25. [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. Zbl0769.05096MR1198383
26. [26] A. Selberg, Bemerkinger om et multipelt integral, Norsk Mathematisk Tidsskrift, Vol. 26, 1944, pp. 71-78. Zbl0063.06870MR18287
27. [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. Zbl0617.05008MR887367
28. [28] D. Williams, Path decomposition and continuity of local time for one-dimensional diffusions, Proc. London Math. Soc., Vol. 28, 1974, pp. 738-768. Zbl0326.60093MR350881
29. [29] D. Zeilberger, Andre's reflection proof generalized to the many-candidate ballot problem, Discrete Math, Vol. 44, 1983, pp. 325-326. Zbl0508.05008MR696297

1. Emmanuel Cépa, Dominique Lépingle, Brownian particles with electrostatic repulsion on the circle : Dyson’s model for unitary random matrices revisited
2. Emmanuel Cépa, Dominique Lépingle, Brownian particles with electrostatic repulsion on the circle: Dyson's model for unitary random matrices revisited
3. Neil O'Connell, Random matrices, non-colliding processes and queues
4. Irina Kurkova, Kilian Raschel, Random walks in ${\left({\mathbb{Z}}_{+}\right)}^2$ with non-zero drift absorbed at the axes