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Matrix models of two-dimensional quantum gravity and isomonodromic solutions of “discrete Painlevé” equations. (English. Russian original) Zbl 0834.58041
J. Math. Sci., New York 73, No. 4, 415-429 (1995); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 187, 3-30 (1991).
See the review in Zbl 0748.58039.

MSC:
58Z05 Applications of global analysis to the sciences
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
39B42 Matrix and operator functional equations
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
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[1] E. Brezin and V. Kazakov,Phys. Lett. B.,236B, 144 (1990).
[2] D. Gross and A. Migdal,Phys. Rev. Lett.,64, 127 (1990). · Zbl 1050.81610 · doi:10.1103/PhysRevLett.64.127
[3] M. Douglas and S. Shenker, ”Strings in less than one dimension,” (Rutgers preprint), No. RU-89-34 (1989).
[4] D. Gross and A. Migdal, ”A nonperturbative treatment of two dimensional quantum gravity,” (Princeton preprint), No. PUPT-1159 (1989).
[5] M. Douglas, ”Strings in less than one dimension and the generalized KdV hierarchies,” (Rutgers preprint), No. RU-89-51 (1989).
[6] T. Banks, M. Douglas, N. Seiberg, and S. Shenker, ”Microscopic and macroscopic loops in non-perturbative two dimensional gravity,” (Rutgers preprint), No. RU-89-50 (1989). · Zbl 1332.81200
[7] O. Alvarez and P. Windey, ”Universality in two dimensional quantum gravity,” (Preprint), Paris VI University, No. PAR-LPTHE 90-12 (1990). · Zbl 0768.58053
[8] E. Brezin, E. Marinari, and G. Parisi, ”A non-perturbative ambiguity free solution of a string model,” (Roma preprint), No. ROM2F-90-09 (1990).
[9] M. Douglas, N. Seiberg, and S. Shenker, ”Flow and instability in quantum gravity,” (Rutgers preprint), No. RU-90-19 (1990).
[10] G. Moore, ”Geometry of the string equations” (Preprint), Yale University, No. YCTP-P4-90 (1990). · Zbl 0727.35134
[11] H. Bateman and A. Erdélyi,Higher Transcendental Functions, Mc Graw-Hill, New York-Toronto-London (1953). · Zbl 0143.29202
[12] A. R. It-s,Izv. Akad. Nauk SSSR, Ser. Mat.,49, No. 3, 530–565 (1985).
[13] A. R. It-s and V. Yu. Novokshenov, ”The isomonodromic deformation method in the theory of Painlevé equations,”Lecture Notes in Math.,1191, Springer-Verlag (1986).
[14] A. R. It-s, A. A. Kapaev, and A. V. Kitaev, in:Problems of Theoretical Physics, III. Elementary Particle Theory. Quantum Mechanics. Mathematical Physics. Statistical Physics [in Russian], LGU, Leningrad, 182–192 (1988).
[15] A. V. Kitaev,Teor. Mat. Fiz.,64, No. 3, 347–369 (1985).
[16] V. I. Gromak,Differents. Uravn.,14, No. 12, 2131–2135 (1978).
[17] A. V. Kitaev,Zapiski Nauch. Sem. LOMI,169, 84–89 (1988).
[18] M. Kac and P. van Moerbeke,Advances in Math.,16, No. 2, 160–169 (1975). · Zbl 0306.34001 · doi:10.1016/0001-8708(75)90148-6
[19] M. Jimbo and T. Miwa,Physica D.,2D, No. 3, 407–448 (1981). · Zbl 1194.34166 · doi:10.1016/0167-2789(81)90021-X
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