Scaling limit of vicious walks and two-matrix model

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 66, Issue 1, 2002, Pages

  Katori, Makoto ^a   Tanemura, Hideki ^b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b CHIBA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION; EIGENVALUES AND EIGENFUNCTIONS; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES; SET THEORY; THERMODYNAMICS;

DIFFUSION SCALING; GAUSSIAN RANDOM MATRICES; MATRIX STRUCTURES; ONE-DIMENSIONAL VICIOUS WALKER MODEL;

BROWNIAN MOVEMENT;

EID: 41349084951     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.011105     Document Type: Article

References (42)

1. M. E. Fisher, J. Stat. Phys. 34, 667 (1984).
2. A. J. Guttmann, A. L. Owczarek, and X. G. Viennot, J. Phys. A 31, 8123 (1998).
3. C. Krattenthaler, A. J. Guttmann, and X. G. Viennot, J. Phys. A 33, 8835 (2000).
4. D. A. Huse and M. E. Fisher, Phys. Rev. B 29, 239 (1984).
5. D. K. Arrowsmith, P. Mason, and J. W. Essam, Physica A 177, 267 (1991).
6. J. W. Essam and A. J. Guttmann, Phys. Rev. E 52, 5849 (1995).
7. I. G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd ed. (Oxford University Press, Oxford, 1995).
8. W. Fulton, Young Tableaux, (Cambridge University Press, Cambridge, 1997).
9. R. P. Stanley, Enumerative Combinatorics (Cambridge University Press, Cambridge, 1999), Vol. 2.
10. W. Fulton and J. Harris, Representation Theory (Springer, New York, 1991).
11. K. Johansson, Commun. Math. Phys. 209, 437 (2000).
12. J. Baik, Commun. Pure Appl. Math. 53, 1385 (2000).
13. T. Nagao and P. J. Forrester, Nucl. Phys. B 620[FS], 551 (2002).
14. See also the earlier works on vicious walks by P. J. Forrester, J. Phys. A 22, L609 (1989);
15. J. Phys. AP. J. Forrester23, 1259 (1990);
16. J. Phys. AP. J. Forrester24, 203 (1991).
17. M. L. Mehta, Random Matrices, 2nd ed. (Academic, New York, 1991).
18. P. Deift, Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach (American Math. Society, Providence, 2000).
19. On a torus another construction of nonintersecting Brownian motions and Dyson’s model was given by H. Spohn in Hydrodynamic Behavior of Interacting Particle Systems, edited by G. Papanicolaou (Springer, Berlin, 1987);
20. H. Spohn, Markov Processes and Related Fields 4, 649 (1998).
21. B. Lindström, Bull. London Math. Soc. 5, 85(1973).
22. I. Gessel and X. G. Viennot, Adv. Math. 58, 300 (1985).
23. J. R. Stembridge, Adv. Math. 83, 96 (1990).
24. A. Pandey and M. L. Mehta, Commun. Math. Phys. 87, 449 (1983).
25. M. L. Mehta and A. Pandey, J. Phys. A 16, 2655 (1983).
26. F. J. Dyson, J. Math. Phys. 3, 1191 (1962).
27. T. H. Baker and P. J. Forrester, Commun. Math. Phys. 188, 175 (1997).
28. I. G. Macdonald, SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 13, 988 (1982).
29. A. Selberg, Norsk Mat. Tidsskrift 26, 71 (1944).
30. S. Mukherji and S. M. Bhattacharjee, J. Phys. A 26, L1139 (1993).
31. S. Mukherji and S. M. Bhattacharjee, Phys. Rev. E 48, 3427 (1993);
32. Phys. Rev. ES. MukherjiS. M. Bhattacharjee52, 3301(E) (1995).
33. D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, 3rd ed. (Springer, New York, 1998).
34. J.-P. Imhof, J. Appl. Probab. 21, 500 (1984).
35. P. J. Forrester, J. Stat. Phys. 56, 767 (1989);
36. J. Stat. Phys.P. J. Forrester76, 331 (1994).
37. Harish-Chandra, Am. J. Math. 79, 87 (1957).
38. C. Itzykson and J.-B. Zuber, J. Math. Phys. 21, 411 (1980).
39. M. L. Mehta, Commun. Math. Phys. 79, 327 (1981).
40. S. Okada, J. Comb. Theory, Ser. A 51, 1 (1989).
41. T. Nagao, M. Katori, and H. Tanemura, e-print cond-mat/0202068.
42. T. Nagao, Nucl. Phys. B 602, 622 (2001).