Discrete Orthogonal Polynomials. (AM-164) : : Asymptotics and Applications (AM-164) /

Discrete Orthogonal Polynomials. (AM-164) : : Asymptotics and Applications (AM-164) / / Kenneth D.T-R McLaughlin, Peter D. Miller, T. Kriecherbauer, J. Baik.

This book describes the theory and applications of discrete orthogonal polynomials--polynomials that are orthogonal on a finite set. Unlike other books, Discrete Orthogonal Polynomials addresses completely general weight functions and presents a new methodology for handling the discrete weights case...

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Superior document:Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
VerfasserIn:
Baik, J.,
Kriecherbauer, T.,
McLaughlin, Kenneth D.T-R,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2007]
©2007
Year of Publication:2007
Edition:Course Book
Language:English
Series:Annals of Mathematics Studies ; 164
Online Access:
Physical Description:1 online resource (184 p.) :; 14 halftones. 6 line illus.
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020 |a 9781400837137 
024 7 |a 10.1515/9781400837137  |2 doi 
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035 |a (OCoLC)979579303 
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041 0 |a eng 
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072 7 |a MAT008000  |2 bisacsh 
082 0 4 |a 515/.55  |2 22 
100 1 |a Baik, J.,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Discrete Orthogonal Polynomials. (AM-164) :  |b Asymptotics and Applications (AM-164) /  |c Kenneth D.T-R McLaughlin, Peter D. Miller, T. Kriecherbauer, J. Baik. 
250 |a Course Book 
264 1 |a Princeton, NJ :   |b Princeton University Press,   |c [2007] 
264 4 |c ©2007 
300 |a 1 online resource (184 p.) :  |b 14 halftones. 6 line illus. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
490 0 |a Annals of Mathematics Studies ;  |v 164 
505 0 0 |t Frontmatter --   |t Contents --   |t Preface --   |t Chapter 1. Introduction --   |t Chapter 2. Asymptotics of General Discrete Orthogonal Polynomials in the Complex Plane --   |t Chapter 3. Applications --   |t Chapter 4. An Equivalent Riemann-Hilbert Problem --   |t Chapter 5. Asymptotic Analysis --   |t Chapter 6. Discrete Orthogonal Polynomials: Proofs of Theorems Stated in §2.3 --   |t Chapter 7. Universality: Proofs of Theorems Stated in §3.3 --   |t Appendix A. The Explicit Solution of Riemann-Hilbert Problem 5.1 --   |t Appendix B. Construction of the Hahn Equilibrium Measure: the Proof of Theorem 2.17 --   |t Appendix C. List of Important Symbols --   |t Bibliography --   |t Index 
506 0 |a restricted access  |u http://purl.org/coar/access_right/c_16ec  |f online access with authorization  |2 star 
520 |a This book describes the theory and applications of discrete orthogonal polynomials--polynomials that are orthogonal on a finite set. Unlike other books, Discrete Orthogonal Polynomials addresses completely general weight functions and presents a new methodology for handling the discrete weights case. J. Baik, T. Kriecherbauer, K. T.-R. McLaughlin & P. D. Miller focus on asymptotic aspects of general, nonclassical discrete orthogonal polynomials and set out applications of current interest. Topics covered include the probability theory of discrete orthogonal polynomial ensembles and the continuum limit of the Toda lattice. The primary concern throughout is the asymptotic behavior of discrete orthogonal polynomials for general, nonclassical measures, in the joint limit where the degree increases as some fraction of the total number of points of collocation. The book formulates the orthogonality conditions defining these polynomials as a kind of Riemann-Hilbert problem and then generalizes the steepest descent method for such a problem to carry out the necessary asymptotic analysis. 
530 |a Issued also in print. 
538 |a Mode of access: Internet via World Wide Web. 
546 |a In English. 
588 0 |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) 
650 0 |a Orthogonal polynomials  |x Asymptotic theory. 
650 0 |a Polynômes orthogonaux  |x Théorie asymptotique. 
650 7 |a MATHEMATICS / Discrete Mathematics.  |2 bisacsh 
653 |a Airy function. 
653 |a Analytic continuation. 
653 |a Analytic function. 
653 |a Ansatz. 
653 |a Approximation error. 
653 |a Approximation theory. 
653 |a Asymptote. 
653 |a Asymptotic analysis. 
653 |a Asymptotic expansion. 
653 |a Asymptotic formula. 
653 |a Beta function. 
653 |a Boundary value problem. 
653 |a Calculation. 
653 |a Cauchy's integral formula. 
653 |a Cauchy-Riemann equations. 
653 |a Change of variables. 
653 |a Complex number. 
653 |a Complex plane. 
653 |a Correlation function. 
653 |a Degeneracy (mathematics). 
653 |a Determinant. 
653 |a Diagram (category theory). 
653 |a Discrete measure. 
653 |a Distribution function. 
653 |a Eigenvalues and eigenvectors. 
653 |a Equation. 
653 |a Estimation. 
653 |a Existential quantification. 
653 |a Explicit formulae (L-function). 
653 |a Factorization. 
653 |a Fredholm determinant. 
653 |a Functional derivative. 
653 |a Gamma function. 
653 |a Gradient descent. 
653 |a Harmonic analysis. 
653 |a Hermitian matrix. 
653 |a Homotopy. 
653 |a Hypergeometric function. 
653 |a I0. 
653 |a Identity matrix. 
653 |a Inequality (mathematics). 
653 |a Integrable system. 
653 |a Invariant measure. 
653 |a Inverse scattering transform. 
653 |a Invertible matrix. 
653 |a Jacobi matrix. 
653 |a Joint probability distribution. 
653 |a Lagrange multiplier. 
653 |a Lax equivalence theorem. 
653 |a Limit (mathematics). 
653 |a Linear programming. 
653 |a Lipschitz continuity. 
653 |a Matrix function. 
653 |a Maxima and minima. 
653 |a Monic polynomial. 
653 |a Monotonic function. 
653 |a Morera's theorem. 
653 |a Neumann series. 
653 |a Number line. 
653 |a Orthogonal polynomials. 
653 |a Orthogonality. 
653 |a Orthogonalization. 
653 |a Parameter. 
653 |a Parametrix. 
653 |a Pauli matrices. 
653 |a Pointwise convergence. 
653 |a Pointwise. 
653 |a Polynomial. 
653 |a Potential theory. 
653 |a Probability distribution. 
653 |a Probability measure. 
653 |a Probability theory. 
653 |a Probability. 
653 |a Proportionality (mathematics). 
653 |a Quantity. 
653 |a Random matrix. 
653 |a Random variable. 
653 |a Rate of convergence. 
653 |a Rectangle. 
653 |a Rhombus. 
653 |a Riemann surface. 
653 |a Special case. 
653 |a Spectral theory. 
653 |a Statistic. 
653 |a Subset. 
653 |a Theorem. 
653 |a Toda lattice. 
653 |a Trace (linear algebra). 
653 |a Trace class. 
653 |a Transition point. 
653 |a Triangular matrix. 
653 |a Trigonometric functions. 
653 |a Uniform continuity. 
653 |a Unit vector. 
653 |a Upper and lower bounds. 
653 |a Upper half-plane. 
653 |a Variational inequality. 
653 |a Weak solution. 
653 |a Weight function. 
653 |a Wishart distribution. 
700 1 |a Kriecherbauer, T.,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
700 1 |a McLaughlin, Kenneth D.T-R,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton Annals of Mathematics eBook-Package 1940-2020  |z 9783110494914  |o ZDB-23-PMB 
773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton University Press eBook-Package Backlist 2000-2013  |z 9783110442502 
776 0 |c print  |z 9780691127347 
856 4 0 |u https://doi.org/10.1515/9781400837137 
856 4 0 |u https://www.degruyter.com/isbn/9781400837137 
856 4 2 |3 Cover  |u https://www.degruyter.com/document/cover/isbn/9781400837137/original 
912 |a 978-3-11-044250-2 Princeton University Press eBook-Package Backlist 2000-2013  |c 2000  |d 2013 
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912 |a ZDB-23-PMB  |c 1940  |d 2020 

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