Discrete Orthogonal Polynomials
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A01=J. Baik
A01=Kenneth D.T-R McLaughlin
A01=Kenneth Dean T-R McLaughlin
A01=Peter D. Miller
A01=T. Kriecherbauer
Analytic continuation
Analytic function
Approximation error
Approximation theory
Asymptote
Asymptotic analysis
Asymptotic formula
Author_J. Baik
Author_Kenneth D.T-R McLaughlin
Author_Kenneth Dean T-R McLaughlin
Author_Peter D. Miller
Author_T. Kriecherbauer
Boundary value problem
Calculation
Category=PB
Cauchy's integral formula
Cauchy-Riemann equations
Change of variables
Complex plane
Correlation function
Degeneracy (mathematics)
Discrete measure
Eigenvalues and eigenvectors
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equation
Explicit formulae (L-function)
Factorization
Fredholm determinant
Functional derivative
Gamma function
Harmonic analysis
Hermitian matrix
Homotopy
Hypergeometric function
I0
Identity matrix
Invariant measure
Inverse scattering transform
Invertible matrix
Jacobi matrix
Joint probability distribution
Lax equivalence theorem
Limit (mathematics)
Linear programming
Lipschitz continuity
Maxima and minima
Monic polynomial
Monotonic function
Morera's theorem
Neumann series
Orthogonal polynomials
Orthogonality
Orthogonalization
Parameter
Parametrix
Pauli matrices
Pointwise
Polynomial
Probability measure
Proportionality (mathematics)
Quantity
Random matrix
Rectangle
Riemann surface
Special case
Spectral theory
Statistic
Subset
Theorem
Toda lattice
Trace (linear algebra)
Transition point
Triangular matrix
Unit vector
Upper half-plane
Variational inequality
Wishart distribution
Product details
- ISBN 9780691127347
- Weight: 369g
- Dimensions: 203 x 254mm
- Publication Date: 22 Jan 2007
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
J. Baik is Associate Professor of Mathematics at the University of Michigan. T. Kriecherbauer is Professor of Mathematics at Ruhr-Universitat Bochum in Bochum, Germany. K. T.-R. McLaughlin is Professor of Mathematics at the University of Arizona. P. D. Miller is Associate Professor of Mathematics at the University of Michigan.
