Asymptotics for Polynomials Orthogonal with Respect to Varying Exponential Weights

International Mathematics Research Notices

Volumn , Issue 16, 1997, Pages

  Deift, P ^a   Kriecherbauer, T ^b   McLaughlin, K T R ^c,d   Venakides, S ^e   Zhou, X ^e,f  

^a NEW YORK UNIVERSITY   (United States)

^b UNIVERSITY OF MUNICH   (Germany)

^c OHIO STATE UNIVERSITY   (United States)

^d PRINCETON UNIVERSITY   (United States)

^e DUKE UNIVERSITY   (United States)

^f INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

[No Author keywords available]

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EID: 1842689760     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (25)

1. M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables, Dover Publications, New York, 1966.
2. S. Albevario, L. Pastur, and M. Shcherbina, On asymptotic properties of certain polynomials, preprint #277, E. Schrodinger Inst., Vienna, 1995.
3. P. Bleher and A. Its, Asymptotics of orthogonal polynomials and universality in matrix models, preprint, 1996.
4. K. Clancey and I. Gohberg, Factorization of Matrix Functions and Singular Integral Operators, Oper. Theory Adv. Appl. 3, Birkhäuser Verlag, Basel, 1981.
5. P. Deift, A.R. Its, and X. Zhou, A Riemann-Hilbert approach to asymptotic problems arising in the theory of random matrix models, and also in the theory of integrable statistical mechanics, Ann. of Math. 145 (1997), 1-88.
6. P. Deift, T. Kriecherbauer, and K. T-R McLaughlin, New results for the asymptotics of orthogonal polynomials and related problems via the inverse spectral method, to appear in J. Approx. Theory.
7. P. Deift, S. Venakides, and X. Zhou, New results in small dispersion KdV by an extension of the steepest descent method for Riemann - Hilbert problems, IMRN (Internat. Math. Res. Notices) 1997, 285-299.
8. P. Deift and X. Zhou, A steepest descent method for oscillatory Riemann - Hilbert problems. Asymptotics for the mKdV equation, Ann. of Math. 137 (1993), 295-368.
9. _, Asymptotics for the Painlevé II equation, Comm. Pure Appl. Math. 48 (1995), 277-337.
10. H. Farkas and I. Kra, Riemann Surfaces, Grad. Texts in Math. 71, Springer-Verlag, New York, 1992.
11. A.S. Fokas, A.R. Its, and A.V. Kitaev, Isomonodromic approach in the theory of two-dimensional quantum gravity, Usp. Matem. Nauk 45 (1990) 135-136 (Russian).
12. _, Discrete Painlevé equations and their appearance in quantum gravity, Comm. Math. Phys. 142 (1991), 313-344.
13. A. R. Its and V. Yu. Novokshenov, The Isomonodromic Deformation Method in the Theory of Painlevé Equations, Lecture Notes in Math. 1191 Springer-Verlag, Berlin, 1986.
14. K. Johansson, On fluctuations of eigenvalues of random Hermitian matrices, to appear in Duke Math. J.
15. N. Katz and P. Sarnak, The spacing distribution between zeros of zeta functions, preprint, 1996.
16. D. Lubinsky, Strong Asymptotics for Extremal Errors and Polynomials Associated with Erdos-type Weights, Pitman Res. Notes Math. Ser. 202, Longman Scientific and Technical, Harlow, UK, 1989.
17. M. L. Mehta, Random Matrices, 2d ed., Academic Press, Boston, 1991.
18. 4), SIAM J. Math. Anal. 15 (1984), 1177-1187.
19. L. A. Pastur, "Spectral and probabilistic aspects of matrix models," in Algebraic and Geometric Methods in Mathematical Phsyics (Kaciveli, 1993), Math. Phys. Stud. 19, Kluwer Acad. Publ., Dordrecht, 1996, 207-242.
20. L. A. Pastur and M. Shcherbina, Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles, J. Stat. Phys. 86 (1997), 109-147.
21. E. A. Rachmanov, "Strong asymptotics for orthogonal polynomials" in Methods of Approximation Theory in Complex Analysis and Mathematical Physics, A. A. Gonchar and E. B. Saff, eds., Nauka, Moscow, 1992, 71-97; Lecture Notes in Math. 1550, Springer-Verlag, Berlin, 1993.
22. E. A. Rachmanov, "Strong asymptotics for orthogonal polynomials" in Methods of Approximation Theory in Complex Analysis and Mathematical Physics, A. A. Gonchar and E. B. Saff, eds., Nauka, Moscow, 1992, 71-97; Lecture Notes in Math. 1550, Springer-Verlag, Berlin, 1993.
23. E. B. Saff and V. Totik, Logarithmic Potentials with External Fields, Springer-Verlag, New York, 1997.
24. 6/6), J. Approx. Theory 50 (1987), 232-293.
25. G. Szego, Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ. 23, American Mathematical Society, New York, 1939.