Ordered random walks

Electronic Journal of Probability

Volumn 13, Issue , 2008, Pages 1307-1336

  Eichelsbacher, Peter ^a   König, Wolfgang ^b  

^a RUHR UNIVERSITY BOCHUM   (Germany)

^b UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

Doob h transform; Dyson s Brownian motions; Fluctuation theory; Non colliding random walks; Non intersecting random processes; Vandermonde determinant

Indexed keywords

EID: 49949095322     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v13-539     Document Type: Article

References (22)

1. J. BAIK, Random vicious walks and random matrices, Comm. Pure Appl. Math. 53, 1385-1410 (2000).
2. J. BAIK and T. SUIDAN, Random matrix central limit theorems for non-intersecting random walks, Ann. Probab. 35, no. 5, 1807-1834 (2007).
3. J. BERTOIN and R. A. DONEY, On conditioning a random walk to stay nonnegative, Ann. Probab. 22:4, 2152-2167 (1994).
4. P. BOUGEROL and T. JEULIN, Paths in Weyl chambers and random matrices, Probab. Theory Related Fields 124:4, 517-543 (2002).
5. M.-F. BRU, Wishart processes, J. Theoret. Probab. 3:4, 725-751 (1991).
6. Y. DOUMERO, Matrices aleatoires, processus stochastiques et groupes de reflexions, PhD thesis, Universite Toulouse (2005).
7. F.J. DYSON, A Brownian-motion model for the eigenvalues of a random matrix, J. Math. Phys. 3, 1191-1198 (1962).
8. W. FELLER, An Introduction to Probability Theory and its Applications, Vol. 2, John Wiley and Sons, New York, 2nd edition (1971).
9. D. GRABINER, Brownian motion in a Weyl chamber, non-colliding particles, and random matrices, Ann. Inst. H. Poincaré Probab. Statist. 35:2, 177-204 (1999).
10. D. HOBSON and W. WERNER, Non-colliding Brownian motion on the circle, Bull. Math. Soc. 28, 643-650 (1996).
11. K. JOHANSSON, Shape fluctuations and random matrices, Commun. Math. Phys. 209, 437-476 (2000).
12. K. JOHANSSON, Non-intersecting paths, random tilings and random matrices, Probab. Theory Related Fields 123:2, 225-280 (2002).
13. S.P. KARLIN and G. MCGREGOR, Coincidence probabilities, Pacif. J. Math. 9, 1141-1164 (1959).
14. M. KATORI and H. TANEMÜRA, Scaling limit of vicious walks and two-matrix model, Phys. Rev. E. 66 011105 (2002).
15. M. KATORI and H. TANEMÜRA, Non-colliding Brownian motions and Harish-Chandra formula, Elec. Commun. Prob. 8, Paper No. 13 (2003).
16. M. KATORI and H. TANEMÜRA, Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems, J. Math. Phys. 45, 3058-3085 (2004).
17. M. KATORI, T. NAGAO and H. TANEMÜRA, Infinite systems of non-colliding Brownian particles, Adv. Stud. Pure Math. 39, 283-306 (2004).
18. W. KÖNIG and N. O'CONNELL, Eigenvalues of the Laguerre process as non-colliding squared Bessel processes, Elec. Comm. Probab. 6, Paper no. 11, 107-114 (2001).
19. W. KÖNIG, N. O'CONNELL and S. ROCH, Non-colliding random walks, tandem queues, and discrete orthogonal polynomial ensembles, Elec. Jour. Probab. 7, Paper no. 5, 1-24 (2002)
20. W. KÖNIG, Orthogonal polynomial ensembles in probability theory, Prob. Surv. 2, 385-447 (2005).
21. N. O'CONNELL, Random matrices, non-colliding processes and queues, Seminaire de Probabilites XXXVI, 165-182, Lecture Notes in Math. 1801, Springer, Berlin (2003).
22. V.V. PETROV, Sums of Independent Random Variables, Springer, Berlin (1975).