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
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Physical Description:1 online resource (184 p.) :; 14 halftones. 6 line illus.
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spelling Baik, J., author. aut http://id.loc.gov/vocabulary/relators/aut
Discrete Orthogonal Polynomials. (AM-164) : Asymptotics and Applications (AM-164) / Kenneth D.T-R McLaughlin, Peter D. Miller, T. Kriecherbauer, J. Baik.
Course Book
Princeton, NJ : Princeton University Press, [2007]
©2007
1 online resource (184 p.) : 14 halftones. 6 line illus.
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
text file PDF rda
Annals of Mathematics Studies ; 164
Frontmatter -- Contents -- Preface -- Chapter 1. Introduction -- Chapter 2. Asymptotics of General Discrete Orthogonal Polynomials in the Complex Plane -- Chapter 3. Applications -- Chapter 4. An Equivalent Riemann-Hilbert Problem -- Chapter 5. Asymptotic Analysis -- Chapter 6. Discrete Orthogonal Polynomials: Proofs of Theorems Stated in §2.3 -- Chapter 7. Universality: Proofs of Theorems Stated in §3.3 -- Appendix A. The Explicit Solution of Riemann-Hilbert Problem 5.1 -- Appendix B. Construction of the Hahn Equilibrium Measure: the Proof of Theorem 2.17 -- Appendix C. List of Important Symbols -- Bibliography -- Index
restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star
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.
Issued also in print.
Mode of access: Internet via World Wide Web.
In English.
Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022)
Orthogonal polynomials Asymptotic theory.
Polynômes orthogonaux Théorie asymptotique.
MATHEMATICS / Discrete Mathematics. bisacsh
Airy function.
Analytic continuation.
Analytic function.
Ansatz.
Approximation error.
Approximation theory.
Asymptote.
Asymptotic analysis.
Asymptotic expansion.
Asymptotic formula.
Beta function.
Boundary value problem.
Calculation.
Cauchy's integral formula.
Cauchy-Riemann equations.
Change of variables.
Complex number.
Complex plane.
Correlation function.
Degeneracy (mathematics).
Determinant.
Diagram (category theory).
Discrete measure.
Distribution function.
Eigenvalues and eigenvectors.
Equation.
Estimation.
Existential quantification.
Explicit formulae (L-function).
Factorization.
Fredholm determinant.
Functional derivative.
Gamma function.
Gradient descent.
Harmonic analysis.
Hermitian matrix.
Homotopy.
Hypergeometric function.
I0.
Identity matrix.
Inequality (mathematics).
Integrable system.
Invariant measure.
Inverse scattering transform.
Invertible matrix.
Jacobi matrix.
Joint probability distribution.
Lagrange multiplier.
Lax equivalence theorem.
Limit (mathematics).
Linear programming.
Lipschitz continuity.
Matrix function.
Maxima and minima.
Monic polynomial.
Monotonic function.
Morera's theorem.
Neumann series.
Number line.
Orthogonal polynomials.
Orthogonality.
Orthogonalization.
Parameter.
Parametrix.
Pauli matrices.
Pointwise convergence.
Pointwise.
Polynomial.
Potential theory.
Probability distribution.
Probability measure.
Probability theory.
Probability.
Proportionality (mathematics).
Quantity.
Random matrix.
Random variable.
Rate of convergence.
Rectangle.
Rhombus.
Riemann surface.
Special case.
Spectral theory.
Statistic.
Subset.
Theorem.
Toda lattice.
Trace (linear algebra).
Trace class.
Transition point.
Triangular matrix.
Trigonometric functions.
Uniform continuity.
Unit vector.
Upper and lower bounds.
Upper half-plane.
Variational inequality.
Weak solution.
Weight function.
Wishart distribution.
Kriecherbauer, T., author. aut http://id.loc.gov/vocabulary/relators/aut
McLaughlin, Kenneth D.T-R, author. aut http://id.loc.gov/vocabulary/relators/aut
Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 9783110442502
print 9780691127347
https://doi.org/10.1515/9781400837137
https://www.degruyter.com/isbn/9781400837137
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language English
format eBook
author Baik, J.,
Baik, J.,
Kriecherbauer, T.,
McLaughlin, Kenneth D.T-R,
spellingShingle Baik, J.,
Baik, J.,
Kriecherbauer, T.,
McLaughlin, Kenneth D.T-R,
Discrete Orthogonal Polynomials. (AM-164) : Asymptotics and Applications (AM-164) /
Annals of Mathematics Studies ;
Frontmatter --
Contents --
Preface --
Chapter 1. Introduction --
Chapter 2. Asymptotics of General Discrete Orthogonal Polynomials in the Complex Plane --
Chapter 3. Applications --
Chapter 4. An Equivalent Riemann-Hilbert Problem --
Chapter 5. Asymptotic Analysis --
Chapter 6. Discrete Orthogonal Polynomials: Proofs of Theorems Stated in §2.3 --
Chapter 7. Universality: Proofs of Theorems Stated in §3.3 --
Appendix A. The Explicit Solution of Riemann-Hilbert Problem 5.1 --
Appendix B. Construction of the Hahn Equilibrium Measure: the Proof of Theorem 2.17 --
Appendix C. List of Important Symbols --
Bibliography --
Index
author_facet Baik, J.,
Baik, J.,
Kriecherbauer, T.,
McLaughlin, Kenneth D.T-R,
Kriecherbauer, T.,
Kriecherbauer, T.,
McLaughlin, Kenneth D.T-R,
McLaughlin, Kenneth D.T-R,
author_variant j b jb
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author_role VerfasserIn
VerfasserIn
VerfasserIn
VerfasserIn
author2 Kriecherbauer, T.,
Kriecherbauer, T.,
McLaughlin, Kenneth D.T-R,
McLaughlin, Kenneth D.T-R,
author2_variant t k tk
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author2_role VerfasserIn
VerfasserIn
VerfasserIn
VerfasserIn
author_sort Baik, J.,
title Discrete Orthogonal Polynomials. (AM-164) : Asymptotics and Applications (AM-164) /
title_sub Asymptotics and Applications (AM-164) /
title_full Discrete Orthogonal Polynomials. (AM-164) : Asymptotics and Applications (AM-164) / Kenneth D.T-R McLaughlin, Peter D. Miller, T. Kriecherbauer, J. Baik.
title_fullStr Discrete Orthogonal Polynomials. (AM-164) : Asymptotics and Applications (AM-164) / Kenneth D.T-R McLaughlin, Peter D. Miller, T. Kriecherbauer, J. Baik.
title_full_unstemmed Discrete Orthogonal Polynomials. (AM-164) : Asymptotics and Applications (AM-164) / Kenneth D.T-R McLaughlin, Peter D. Miller, T. Kriecherbauer, J. Baik.
title_auth Discrete Orthogonal Polynomials. (AM-164) : Asymptotics and Applications (AM-164) /
title_alt Frontmatter --
Contents --
Preface --
Chapter 1. Introduction --
Chapter 2. Asymptotics of General Discrete Orthogonal Polynomials in the Complex Plane --
Chapter 3. Applications --
Chapter 4. An Equivalent Riemann-Hilbert Problem --
Chapter 5. Asymptotic Analysis --
Chapter 6. Discrete Orthogonal Polynomials: Proofs of Theorems Stated in §2.3 --
Chapter 7. Universality: Proofs of Theorems Stated in §3.3 --
Appendix A. The Explicit Solution of Riemann-Hilbert Problem 5.1 --
Appendix B. Construction of the Hahn Equilibrium Measure: the Proof of Theorem 2.17 --
Appendix C. List of Important Symbols --
Bibliography --
Index
title_new Discrete Orthogonal Polynomials. (AM-164) :
title_sort discrete orthogonal polynomials. (am-164) : asymptotics and applications (am-164) /
series Annals of Mathematics Studies ;
series2 Annals of Mathematics Studies ;
publisher Princeton University Press,
publishDate 2007
physical 1 online resource (184 p.) : 14 halftones. 6 line illus.
Issued also in print.
edition Course Book
contents Frontmatter --
Contents --
Preface --
Chapter 1. Introduction --
Chapter 2. Asymptotics of General Discrete Orthogonal Polynomials in the Complex Plane --
Chapter 3. Applications --
Chapter 4. An Equivalent Riemann-Hilbert Problem --
Chapter 5. Asymptotic Analysis --
Chapter 6. Discrete Orthogonal Polynomials: Proofs of Theorems Stated in §2.3 --
Chapter 7. Universality: Proofs of Theorems Stated in §3.3 --
Appendix A. The Explicit Solution of Riemann-Hilbert Problem 5.1 --
Appendix B. Construction of the Hahn Equilibrium Measure: the Proof of Theorem 2.17 --
Appendix C. List of Important Symbols --
Bibliography --
Index
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callnumber-first Q - Science
callnumber-subject QA - Mathematics
callnumber-label QA404
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illustrated Illustrated
dewey-hundreds 500 - Science
dewey-tens 510 - Mathematics
dewey-ones 515 - Analysis
dewey-full 515/.55
dewey-sort 3515 255
dewey-raw 515/.55
dewey-search 515/.55
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code="a">Random matrix.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Random variable.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Rate of convergence.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Rectangle.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Rhombus.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Riemann surface.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Special case.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Spectral theory.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Statistic.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Subset.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Theorem.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Toda lattice.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Trace (linear algebra).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Trace class.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Transition point.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Triangular matrix.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Trigonometric functions.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Uniform continuity.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Unit vector.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Upper and lower bounds.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Upper half-plane.</subfield></datafield><datafield tag="653" ind1=" " 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