Random walks in (Z+)2 with non-zero drift absorbed at the axes

Bulletin de la Societe Mathematique de France

Volumn 139, Issue 3, 2011, Pages 341-387

  Kurkova, Irina ^a   Raschel, Kilian ^b  

^a SORBONNE UNIVERSITÉ   (France)

^b UNIVERSITÉ DE TOURS   (France)

Author keywords

Absorption probabilities; Green functions; Holomorphic continuation; Random walk; Singularities of complex functions; Steepest descent method

Indexed keywords

EID: 84860608035     PISSN: 00379484     EISSN: None     Source Type: Journal    
DOI: 10.24033/bsmf.2611     Document Type: Article

References (31)

1. P. BIANE - "Quantum random walk on the dual of SU(n)", Probab. Theory Related Fields 89 (1991), p. 117-129.
2. -, "Frontière de Martin du dual de SU(2)", in Séminaire de Probabilités, XXVI, Lecture Notes in Math., vol. 1526, Springer, 1992, p. 225-233.
3. -, "Minuscule weights and random walks on lattices", in Quantum probability & related topics, QP-PQ, VII, World Sci. Publ., River Edge, NJ, 1992, p. 51-65.
4. M. BOUSQUET-MELOU & M. MISHNA - "Walks with small steps in the quarter plane", in Algorithmic probability and combinatorics, Contemp. Math., vol. 520, Amer. Math. Soc, 2010, p. 1-39.
5. M.-F. BRU - "Wishart processes", J. Theoret. Probab. 4 (1991), p. 725-751.
6. B. CHABAT - Introduction à l'analyse complexe. Tome 1, Traduit du Russe: Mathématiques., "Mir", 1990.
7. F. J. DYSON - "A Brownian-motion model for the eigenvalues of a random matrix", J. Mathematical Phys. 3 (1962), p. 1191-1198.
8. P. EICHELSBACHER & W. KÖNIG - "Ordered random walks", Electron. J. Probab. 13 (2008), p. no. 46, 1307-1336.
9. G. FAYOLLE, R. IASNOGORODSKI & V. A. MALYSHEV - Random walks in the quarter-plane, Applications of Mathematics (New York), vol. 40, Springer, 1999.
10. M. V. FEDORYUK - "Asymptotic methods in analysis", in Current problems of mathematics. Fundamental directions, Vol. 13 (Russian), Itogi Nauki i Tekhniki, Akad. Nauk SSSR Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., 1986, p. 93-210.
11. D. J. GRABINER - "Brownian motion in a Weyl chamber, non-colliding particles, and random matrices", Ann. Inst. H. Poincaré Probab. Statist. 35 (1999), p. 177-204.
12. P.-L. HENNEQUIN - "Processus de Markoff en cascade", Ann. Inst. H. Poincaré 18 (1963), p. 109-195.
13. D. G. HOBSON & W. WERNER - "Non-colliding Brownian motions on the circle", Bull. London Math. Soc. 28 (1996), p. 643-650. (Pubitemid 126383001)
14. I. IGNATIOUK-ROBERT - "Martin boundary of a killed random walk on a half-space", J. Theoret. Probab. 21 (2008), p. 35-68.
15. -, "Martin boundary of a reflected random walk on a half-space", Probab. Theory Related Fields 148 (2010), p. 197-245.
16. I. IGNATIOUK-ROBERT & C. LOREE - "Martin boundary of a killed random walk on a quadrant", Ann. Probab. 38 (2010), p. 1106-1142.
17. K. JOHANSSON-"Shape fluctuations and random matrices", Comm. Math. Phys. 209 (2000), p. 437-476.
18. -, "Non-intersecting paths, random tilings and random matrices", Probab. Theory Related Fields 123 (2002), p. 225-280. (Pubitemid 36195084)
19. M. KATORI & H. TANEMURA - "Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems", J. Math. Phys. 45 (2004), p. 3058-3085. (Pubitemid 39223874)
20. W. KÖNIG & N. O'CONNELL - "Eigenvalues of the Laguerre process as non-colliding squared Bessel processes", Electron. Comm. Probab. 6 (2001), p. 107-114. (Pubitemid 38818002)
21. W. KÖNIG, N. O'CONNELL & S. ROCH - "Non-colliding random walks, tandem queues, and discrete orthogonal polynomial ensembles", Electron. J. Probab. 7 (2002), p. no. 5, 24 pp.
22. I. A. KURKOVA & V. A. MALYSHEV - "Martin boundary and elliptic curves", Markov Process. Related Fields 4 (1998), p. 203-272.
23. J. K. Lu - Boundary value problems for analytic functions, Series in Pure Mathematics, vol. 16, World Scientific Publishing Co. Inc., 1993.
24. V. A. MALYSHEV - "An analytical method in the theory of two-dimensional positive random walks", Sib. Math. J. 13 (1972), p. 917-929.
25. -, "Asymptotic behavior of the stationary probabilities for two-dimensional positive random walks", Sib. Math. J. 14 (1973), p. 109-118.
26. N. O'CONNELL - "Conditioned random walks and the RSK correspondence", J. Phys. A 36 (2003), p. 3049-3066. (Pubitemid 37347050)
27. -, "A path-transformation for random walks and the Robinson- Schensted correspondence", Trans. Amer. Math. Soc. 355 (2003), p. 3669-3697. (Pubitemid 37056466)
28. -, "Random matrices, non-colliding processes and queues", in Séminaire de Probabilités, XXXVI, Lecture Notes in Math., vol. 1801, Springer, 2003, p. 165-182.
29. N. O'CONNELL & M. YOR - "A representation for non-colliding random walks", Electron. Coram. Probab. 1 (2002), p. 1-12. (Pubitemid 38817982)
30. K. RASCHEL - "Random walks in the quarter plane absorbed at the boundary: Exact and asymptotic", preprint arXiv:0902.2785.
31. G. SANSONE & J. GERRETSEN - Lectures on the theory of functions of a complex variable. II: Geometric theory, Wolters-Noordhoff Publishing, Groningen, 1969.