|
|
|
References
|
|
|
1. |
V. Korepin, P. Zinn-Justin, “Thermodynamic limit of the six-vertex model with domain wall boundary conditions”, J. Phys. A, 33 (2000), 7053 |
2. |
A. V. Razumov, Yu. G. Stroganov, “Spin chains and combinatorics”, J. Phys. A, 34 (2001), 3185 |
3. |
M. T. Batchelor, J. de Gier, B. Nienhuis, “The quantum symmetric XXZ chain at $\Delta=-1/2$, alternating sign matrices and plane partitions”, J. Phys. A, 34 (2001), L265 |
4. |
N. M. Bogoliubov, A. G. Pronko, M. B. Zvonarev, “Boundary correlation functions of the six-vertex model”, J. Phys. A, 35 (2002), 5525 |
5. |
F. Colomo, A. G. Pronko, “Square ice, alternating sign matrices and classical orthogonal polynomials”, J. Stat. Mech., 0501 (2005), P01005 |
6. |
L. D. Faddeev, “Quantum inverse scattering method”, Sov. Sci. Rev. Math., C1 (1980), 107 |
7. |
P. P. Kulish, E. K. Sklyanin, “Quantum spectral transform method. Recent developments”, Springer Lect. Notes Phys., 151, Springer, Berlin–New York, 1981, 61 |
8. |
V. E. Korepin, N. M. Bogoliubov, A. G. Izergin, Quantum Inverse Scattering Method and Correlation Functions, Cambridge Univ. Press, Cambridge, 1993 |
9. |
N. M. Bogoliubov, “Boxed plane partitions as an exactly solvable boson model”, J. Phys. A Math. Gen., 38 (2005), 9415 |
10. |
N. M. Bogoliubov, “Enumeration of plane partitions and algebraic Bethe ansatz”, Theor. Mat. Phys., 150 (2007), 165 |
11. |
G. E. Andrews, The Theory of Partitions, Cambridge Univ. Press, Cambridge, 1998 |
12. |
D. M. Bressoud, Proofs and Confirmations. The Story of the Alternating Sign Matrix Conjecture, Cambridge Univ. Press, Cambridge, 1999 |
13. |
I. G. Macdonald, Symmetric Functions and Hall Polynomials, Clarendon Press, Oxford Univ. Press, New York, 1995 |
14. |
A. Vershik, “Statistical mechanics of combinatorial partitions and their limit configurations”, Funct. Anal. Appl., 30 (1996), 90 |
15. |
A. Vershik, S. Kerov, “Asymptotics of the Plancherel measure of the symmetric group and the limit form of Young tableaux”, Soviet Math. Dokl., 18 (1977), 527 |
16. |
A. Okounkov, N. Reshetikhin, “Correlation function of Schur process with application to local geometry of a random three-dimensional Young diagram”, J. Amer. Math. Soc., 16 (2003), 58 |
17. |
N. M. Bogoliubov, R. K. Bullough, G. D. Pang, “Exact solution of the $q$-boson hopping model”, Phys. Rev. B, 47 (1993), 11495 |
18. |
N. M. Bogoliubov, R. K. Bullough, J. Timonen, “Critical behavior for correlated strongly coupled boson systems in $1+1$-dimensions”, Phys. Rev. Lett., 25 (1994), 3933 |
19. |
N. M. Bogoliubov, A. G. Izergin, N. A. Kitanine, “Correlation functions for a strongly correlated boson systems”, Nucl. Phys. B, 516 (1998), 501 |
20. |
N. Tsilevich, “Quantum inverse scattering method for the $q$-boson model and symmetric functions”, Funct. Anal. Appl., 40 (2006), 53 |
21. |
K. Shigechi, M. Uchiyama, “Boxed skew plane partition and integrable phase model”, J. Phys. A Math. Gen., 38 (2005), 10287 |
22. |
M. E. Fisher, “Walks, walls, wetting and melting”, J. Stat. Phys., 34 (1984), 667 |
23. |
P. J. Forrester, “Exact solution of the lock step model of vicious walkers”, J. Phys. A Math. Gen., 23 (1990), 1259 |
24. |
T. H. Baker, P. J. Forrester, “Random walks and random fixed-point free involutions”, J. Phys. A Math. Gen., 34 (2001), L381 |
25. |
P. J. Forrester, “Random walks and random permutations”, J. Phys. A Math. Gen., 34 (2001), L417 |
26. |
A. J. Guttmann, A. L. Owczarec, X. G. Viennot, “Vicious walkers and Young tableaux. I. Without walls”, J. Phys. A Math. Gen., 31 (1998), 8123 |
27. |
C. Krattenthaler, A. J. Guttmann, X. G. Viennot, “Vicious walkers, friendly walkers and Young tableaux. II. With a wall”, J. Phys. A Math. Gen., 33 (2000), 8835 |
28. |
C. Krattenthaler, A. J. Guttmann, X. G. Viennot, “Vicious walkers, friendly walkers and Young tableaux. III. Between two walls”, J. Stat. Phys., 110 (2003), 1069 |
29. |
T. Tsuchiya, M. Katori, “Chiral Potts models, friendly walkers and directed percolation problem”, J. Phys. Soc. Japan, 67 (1988), 1655 |
30. |
M. Katori, H. Tanemura, “Scaling limit of vicious walks and two-matrix model”, Phys. Rev. E, 66 (2002), 011105 |
31. |
M. Katori, H. Tanemura, T. Nagao, N. Komatsuda, “Vicious walk with a wall, noncolliding meanders, chiral and Bogoliubov–de Gennes random matrices”, Phys. Rev. E, 68 (2003), 021112 |
32. |
N. M. Bogoliubov, “$XXO$ Heisenberg chain and random walks”, Zap. Nauchn. Semin. POMI, 325, 2005, 13 |
33. |
N. M. Bogoliubov, “Integrable models for the vicious and friendly walkers”, Zap. Nauchn. Semin. POMI, 335, 2006, 59 |
34. |
P. Carruters, M. Nieto, “Phase and angle variables in quantum mechanics”, Rev. Mod. Phys., 40 (1968), 411 |
35. |
G. Kuperberg, “Another proof of the alternating-sign matrix conjecture”, Int. Math. Res. Not., 1996 (1996), 139 |