@article{ZNSL_2005_325_a1,
author = {N. M. Bogolyubov},
title = {$XX0$ {Heisenberg} chain and random walks},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {13--27},
year = {2005},
volume = {325},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_325_a1/}
}
N. M. Bogolyubov. $XX0$ Heisenberg chain and random walks. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XII, Tome 325 (2005), pp. 13-27. http://geodesic.mathdoc.fr/item/ZNSL_2005_325_a1/
[1] M. E. Fisher, “Walks, walls, wetting and melting”, J. Statist. Phys., 34 (1984), 667–729 | DOI | MR
[2] P. J. Forrester, “Exact solution of the lock step model of vicious walkers”, J. Phys. A, 23 (1990), 1259–1273 | DOI | MR | Zbl
[3] P. J. Forrester, Random walks and random permutations, arXiv: /math/9907037 | MR
[4] T. Nagao, P. J. Forrester, “Vicious random walkers and a discretization of Gaussian random matrix ensembles”, Nuclear Phys. B, 620 (2002), 551–565 | DOI | MR | Zbl
[5] A. J. Guttmann, A. L. Owczarek, X. G. Viennot, “Vicious walkers and Young tableaux. I: Without walls”, J. Phys. A, 31 (1998), 8123–8135 | DOI | MR | Zbl
[6] C. Krattenthaler, A. J. Guttmann, X. G. Viennot, “Vicious walkers, friendly walkers and Young tableaux. II: With a wall”, J. Phys. A, 33 (2000), 8835–8866 | DOI | MR | Zbl
[7] C. Krattenthaler, A. J. Guttmann, X. G. Viennot, “Vicious walkers, friendly walkers and Young tableaux. III: Between two walls”, J. Statist. Phys., 110 (2003), 1069–1086 | DOI | MR | Zbl
[8] M. Katori, H. Tanemura, “Scaling limit of vicious walks and two-matrix model”, Phys. Rev. E, 66 (2002), 011105 | DOI
[9] M. Katori, H. Tanemura, T. Nagao, N. Komatsuda, Vicious walk with a wall, noncolliding meanders, chiral and Bogoliubov–de Gennes random matrices, arXiv: /cond-mat/0303573
[10] D. Huse, M. Fisher, “Commensurate melting, domain walls, and dislocations”, Phys. Rev. B, 29 (1984), 239–270 | DOI | MR
[11] E. Domany, W. Kinzel, “Equivalence of cellular automata to Ising models and directed percolation”, Phys. Rev. Lett., 53 (1984), 311–314 | DOI | MR | Zbl
[12] P. Bak, C. Tang, K. Wiesenfeld, “Self-organized criticality, an explanation of $1/f$ noise”, Phys. Rev. A, 38 (1988), 364–374 | DOI | MR
[13] J. W. Essam, A. J. Guttmann, “Vicious walkers and directed polymer networks in general dimensions”, Phys. Rev. E, 52 (1995), 5849–5862 | DOI | MR
[14] K. Johansson, “Shape fluctuations and random matrices”, Comm. Math. Phys., 209 (2000), 437–476 | DOI | MR | Zbl
[15] M. Prähofer, H. Spohn, “Universal distributions for Growth Processes in 1+1 dimensions and random matrices”, Phys. Rev. Lett., 84 (2000), 4882–4885 | DOI
[16] I. Makdonald, Simmetricheskie funktsii i mnogochleny Kholla, Mir, M., 1985 | MR
[17] M. L. Mehta, Random Matrices, Academic, New-York, 1991 | MR | Zbl
[18] C. Jordan, Calculus of Finite Differences, Chelsea Publ. Comp., New York, 1965 | MR | Zbl