zbMATH — the first resource for mathematics

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.

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
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.