Applications of universality limits to zeros and reproducing kernels of orthogonal polynomials

Journal of Approximation Theory

Volumn 150, Issue 1, 2008, Pages 69-95

  Levin, Eli ^a   Lubinsky, Doron S ^b  

^a OPEN UNIVERSITY OF ISRAEL   (Israel)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 37349108778     PISSN: 00219045     EISSN: 10960430     Source Type: Journal    
DOI: 10.1016/j.jat.2007.05.003     Document Type: Article

References (26)

1. Baik J., Kriecherbauer T., McLaughlin K., and Miller P. Uniform asymptotics for polynomials orthogonal with respect to a general class of discrete weights and universality results for associated ensembles: announcement of results. Internat. Math. Res. Notices 15 (2003) 821-858
2. Baik J., Kriecherbauer T., McLaughlin K., and Miller P. Uniform Asymptotics for Polynomials Orthogonal With Respect to a General Class of Discrete Weights and Universality Results for Associated Ensembles, Annals of Mathematics Studies vol. 164 (2007), Princeton University Press, Princeton
3. Bleher P., and Its I. Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model. Ann. of Math. 150 (1999) 185-266
4. Deift P. Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, Courant Institute Lecture Notes vol. 3 (1999), New York University Press, New York
5. P. Deift, Riemann-Hilbert methods in the theory of orthogonal polynomials, in: F. Gesztesy et al., (Eds.), Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday, Oxford University Press, 2007.
6. Deift P., Kriecherbauer T., McLaughlin K.T.-R., Venakides S., and Zhou X. Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory. Comm. Pure Appl. Math. 52 (1999)
7. Dombrowski J., and Nevai P. Orthogonal polynomials, measures, and recurrence relations. SIAM J. Math. Anal. 17 (1986) 752-759
8. Freud G. Orthogonal Polynomials (1971), Akadémiai Kiadó, Budapest
9. Freud G. On Markov-Bernstein type inequalities and their applications. J. Approx. Theory 19 (1977) 22-37
10. Kuijlaars A.B., and Vanlessen M. Universality for eigenvalue correlations from the modified jacobi unitary ensemble. Internat. Math. Res. Notices 30 (2002) 1575-1600
11. Y. Last, B. Simon, Fine structure of the zeros of orthogonal polynomials, IV. A priori bounds and clock behavior, Comm. Pure Appl. Math., to appear.
12. Levin E., and Lubinsky D.S. Orthogonal Polynomials for Exponential Weights (2001), Springer, New York
13. E. Levin, D.S. Lubinsky, Universality limits for exponential weights, manuscript, 〈http://www.math.gatech.edu/∼lubinsky/Research%20papers/UniversExponMar07.pdf〉.
14. D.S. Lubinsky, A new approach to universality limits involving orthogonal polynomials, Ann. of Math., to appear, 〈http://www.math.gatech.edu/∼lubinsky/Research%20papers/UniversBulkJan07.pdf〉.
15. D.S. Lubinsky, A new approach to universality limits at the edge of the spectrum, in: J. Back et al., (Ed.), Proceedings of the Conference on integrable Systems, Random Matrices and Applications, to appear 〈http://www.math.gatech.edu/∼lubinsky/Research%20papers/UniversEdgeJan07Vn2.pdf〉.
16. Mehta M.L. Random Matrices. second ed. (1991), Academic Press, Boston
17. Mhaskar H.N. Introduction to the Theory of Weighted Polynomial Approximation (1996), World Scientific, Singapore
18. P. Nevai, Orthogonal Polynomials, Memoirs of the AMS, no. 213, 1979.
19. Nevai P., Zhang J., and Totik V. Orthogonal polynomials: their growth relative to their sums. J. Approx. Theory 67 (1991) 215-234
20. Pastur L., and Shcherbina M. Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles. J. Statist. Phys. 86 (1997) 109-147
21. Simon B. Orthogonal Polynomials on the Unit Circle, Parts 1 and 2 (2005), American Mathematical Society, Providence
22. Simon B. Fine structure of the zeros of orthogonal polynomials, III. Periodic recursion coefficients. Comm. Pure Appl. Math. 59 (2005) 1042-1062
23. Simon B. Fine structure of the zeros of orthogonal polynomials, I. A tale of two pictures. Electron. Trans. Numer. Anal. 25 (2006) 328-368
24. Saff E.B., and Totik V. Logarithmic Potentials with External Fields (1997), Springer, New York
25. Stahl H., and Totik V. General Orthogonal Polynomials (1992), Cambridge University Press, Cambridge
26. G. Szego{combining double acute accent}, Orthogonal polynomials, fourth ed., American Mathematical Society Colloquium Publications, vol. 23, American Mathematical Soceity, Providence, 1975.