Integrable models for vicious and friendly walkers

Journal of Mathematical Sciences

Volumn 143, Issue 1, 2007, Pages 2729-2737

  Bogoliubov, N M ^a  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34247394520     PISSN: 10723374     EISSN: 15738795     Source Type: Journal    
DOI: 10.1007/s10958-007-0160-z     Document Type: Article

References (22)

1. P. J. Forrester, "Exact solution of the lock step model of vicious walkers," J. Phys. A.: Math. Gen., 23, 1259 (1990).
2. T. H. Baker and P. J. Forrester, "Random walks and random fixed-point free involutions," J. Phys. A.: Math. Gen., 34, L381 (2001).
3. P. J. Forrester, "Random walks and random permutations," J. Phys. A.: Math. Gen., 34, L417 (2001).
4. T. Nagao and P. J. Forrester, "Vicious random walkers and a discretization of Gaussian random matrix ensembles," Nucl. Phys. B, 620, 551 (2002).
5. J. W. Essam and A. J. Guttmann, "Vicious walkers and directed polymer networks in general dimensions," Phys. Rev. E, 52, 5849 (1995).
6. A. J. Guttmann, A. L. Owczarec, and X. G. Viennot, "Vicious walkers and Young tableaux. I: Without walls," J. Phys. A: Math. Gen., 31, 8123 (1998).
7. C. Krattenthaler, A. J. Guttmann, and X. G. Viennot, "Vicious walkers, friendly walkers, and Young tableaux. II: With a wall," J. Phys. A: Math. Gen., 33, 8835 (2000).
8. C. Krattenthaler, A. J. Guttmann, and X. G. Viennot, "Vicious walkers, friendly walkers, and Young tableaux. III: Between two walls," J. Stat. Phys., 110, 1069 (2003).
9. T. Tsuchiya and M. Katori, "Chiral Potts models, friendly walkers, and directed percolation problem," J. Phys. Soc. Japan, 67, 1655 (1988).
10. M. Katori and H. Tanemura, "Scaling limit of vicious walks and two-matrix model," Phys. Rev. E, 66, 011105 (2002).
11. M. Katori, H. Tanemura, T. Nagao, and N. Komatsuda, "Vicious walk with a wall, noncolliding meanders, chiral and Bogoliubov-de Gennes random matrices," Phys. Rev. E, 68, 021112 (2003).
12. M. Katori and H. Tanemura, "Functional central limit theorems for vicious walkers," (2004); math.PR/0203286.
13. N. M. Bogoliubov, "Boxed plane partitions as an exactly solvable boson model," J. Phys. A: Math. Gen., 38, 9415 (2005).
14. N. M. Bogoliubov, "Enumeration of plane partitions and algebraic Bethe ansatz," Preprint POMI-04/2006.
15. D. M. Bressoud, Proofs and Confirmations. The Story of the Alternating Sign Matrix Conjecture. Cambridge University Press, Cambridge (1999).
16. M. E. Fisher, "Walks, walls, wetting, and melting," J. Stat. Phys., 34, 667 (1984).
17. N. M. Bogoliubov, "XXO Heisenberg chain and random walks," Zap. Nauchn. Semin. POMI, 325, 13 (2005).
18. F. Colomo, A. G. Izergin, V. E. Korepin, and V. Tognetti, "Temperature correlation functions in the XXO Heisenberg chain," Teor. Mat. Fiz., 94, 19 (1993).
19. I. G. Macdonald, Symmetric Functions and Hall Polynomials, Clarendon Press (1995).
20. N. M. Bogoliubov, R. K. Bullough, and G. Pang, "Exact solution of the q-boson hopping model," Phys. Rev. B, 47, 11495 (1993).
21. N. M. Bogoliubov, R. K. Bullough, and J. Timonen, "Critical behavior for correlated strongly coupled boson systems in 1+1 dimensions," Phys. Rev. Lett., 25, 3933 (1994).
22. N. M. Bogoliubov, A. G. Izergin, and N. A. Kitanine, "Correlation functions for a strongly correlated boson systems," Nucl. Phys. B, 516, 501 (1998).