Download this PDF file Fullscreen Fullscreen Off
References
- A. Altland and M. R. Zirnbauer, Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures, Phys. Rev. B 55, 1142-1161 (1997). Math. Review number not available.
- M. F. Bru, Diffusions of perturbed principal component analysis, J. Maltivated Anal. 29, 127-136 (1989). MR 90k:62123
- M. F. Bru, Wishart process, J. Theoret. Probab. 3, 725-751 (1991). MR 93b:60176
- J. L. Doob, Classical Potential Theory and its Probabilistic Counterpart, Springer, 1984. MR 85k:31001
- F. J. Dyson, A Brownian-motion model for the eigenvalues of a random matrix, J. Math. Phys. 3, 1191-1198 (1962). MR 26 #5904
- W. Fulton and J. Harris, Representation Theory, Springer, New York 1991. MR 93a:20069
- D. J. Grabiner, Brownian motion in a Weyl chamber, non-colliding particles, and random matrices, Ann. Inst. Henri Poincar'e 35, 177-204 (1999). MR 2000i:60091
- Harish-Chandra, Differential operators on a semisimple Lie algebra, Am. J. Math. 79, 87-120 (1957). MR 18,809d
- J. P. Imhof, Density factorizations for Brownian motion, meander and the three-dimensional Bessel process, and applications, J. Appl. Prob. 21, 500-510 (1984). MR 85j:60152
- C. Itzykson and J.-B. Zuber, The planar approximation. II, J. Math. Phys. 21, 411-421 (1980). MR 81a:81068
- S. Karlin and L. McGregor, Coincidence properties of birth and death processes, Pacific J. 9, 1109-1140 (1959). MR 22 #5071
- S. Karlin and L. McGregor, Coincidence probabilities, Pacific J. 9, 1141-1164 (1959). MR 22 #5072
- M. Katori, T. Nagao and H. Tanemura, Infinite systems of non-colliding Brownian particles, to be published in Adv. Stud. Pure Math. ``Stochastic Analysis on Large Scale Interacting Systems", Mathematical Society of Japan. (2003). Math. Review number not available.
- M. Katori and H. Tanemura, Scaling limit of vicious walks and two-matrix model, Phys. Rev. E 66, 011105 (2002). Math. Review number not available.
- M. Katori and H. Tanemura, Functional central limit theorems for vicious walkers to appear in Stoch. Stoch. Rep. Math. Review number not available.
- M. Katori and H. Tanemura, in preparation. Math. Review number not available.
- M. Katori, H. Tanemura, T. Nagao and N. Komatsuda, Vicious walk with a wall, noncolliding meanders, and chiral and Bogoliubov-deGennes random matrices, Phys. Rev. E 68, 021112 (2003). Math. Review number not available.
- W. K"{o}nig, and N. O'Connell, Eigenvalues of the Laguerre process as non-colliding squared Bessel processes, Elect. Comm. in Probab. 6, 107-114 (2001). MR 2002j:15025
- M. L. Mehta, Random Matrices, Academic Press, London 1991 (2nd ed.). MR 92f:82002
- M. L. Mehta and A. Pandey, On some Gaussian ensemble of Hermitian matrices, J. Phys. A: Math. Gen. 16, 2655-2684 (1983). MR 85h:81082
- T. Nagao, M. Katori and H. Tanemura, Dynamical correlations among vicious random walkers, Phys. Lett. A 307, 29-35 (2003). MR 1 969 523
- A. Pandey and M. L. Mehta, Gaussian ensembles of random Hermitian matrices intermediate between orthogonal and unitary ones, Commun. Math. Phys. 87, 449-468 (1983). MR 84e:81085
- D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, Springer, 1998 (3rd ed.). MR 2000h:60050
- M. Yor, Some Aspects of Brownian Motion, Part I: Some Special Functionals, Birkh"auser, Basel 1992. MR 93i:60155
- M. R. Zirnbauer, Riemannian symmetric superspaces and their origin in random-matrix theory, J. Math. Phys. 37, 4986-5018 (1996). MR 97m:58012

This work is licensed under a Creative Commons Attribution 3.0 License.