Non-hermitian tridiagonal random matrices and returns to the origin of a random walk

Journal of Statistical Physics

Volumn 98, Issue 3-4, 2000, Pages 685-699

  Cicuta, G M ^a   Contedini, M ^a   Molinari, L ^b  

^a UNIVERSITY OF PARMA   (Italy)

^b UNIVERSITY OF MILAN   (Italy)

Author keywords

Band random matrices; Non hermetian random matrices; Random walks

Indexed keywords

EID: 0034134592     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1018671308053     Document Type: Article

References (16)

1. M. L. Mehta, Random Matrices, 2nd ed., Academic Press, 1991.
2. T. Guhr, A. Muller-Groeling, and H. A. Weidenmüller, Phys. Rep. 299:190 (1998).
3. C. W. J. Beenakker, Rev. Mod. Phys. 69:731 (1977).
4. Lecture notes, preprints and video lectures are available at the site http:/www.msri.org after the recent six-months workshop on Random Matrix Theory at the Mathematical Science Research Institute (1999).
5. F. J. Dyson, Phys. Rev. 92:1331 (1953).
6. H. Schmidt, Phys. Rev. 105:425 (1957).
7. N. Hatano and D. R. Nelson, Phys. Rev. Lett. 77:570 (1996); Phys. Rev. B 56:8651 (1997).
8. N. Hatano and D. R. Nelson, Phys. Rev. Lett. 77:570 (1996); Phys. Rev. B 56:8651 (1997).
9. J. Feinberg and A. Zee, cond-mat/9710040.
10. I. Y. Goldsheid and B. A. Khoruzhenko, Phys. Rev. Lett. 80:2897 (1998).
11. C. Mudry, P. W. Brouwer, B. I. Halperin, V. Gurarie, and A. Zee, Phys. Rev. B 58:13539 (1998).
12. J. Ginibre, J. Math. Phys. 6:440 (1965).
13. H. J. Sommers, A. Crisanti, H. Sompolinski, and Y. Stein, Phys. Rev. Lett. 60:1895 (1988).
14. J. Feinberg and A. Zee, cond-mat/9706218 (1997).
15. The combinatorial analysis of returns to the origin for random walks visiting each site an even number of times, was already presented by G. M. Cicuta and M. Contedini in the preprint math.PR/9903063 (1999).
16. B. Derrida, J. L. Jacobsen, and R. Zeitak, cond-mat/9906235 (1999).