Log-Gases and Random Matrices (LMS-34)
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Asymptotic formula
Author_Peter J. Forrester
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Bidiagonal matrix
Binomial coefficient
Calculation
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Central limit theorem
Change of variables
Characteristic polynomial
Coefficient
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Correlation function
Correlation function (quantum field theory)
Cumulative distribution function
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Determinant
Diagram (category theory)
Differential equation
Dirac equation
Dirac operator
Eigenfunction
Eigenvalues and eigenvectors
Elliptic function
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Equation
Euler's formula
Explicit formulae (L-function)
Factorization
Fredholm determinant
Gamma function
Geometric distribution
Haar measure
Hecke algebra
Hermite polynomials
Hermitian matrix
Hessenberg matrix
Integer matrix
Integral equation
Jacobi polynomials
Joint probability distribution
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Laplace's equation
Lattice path
Nucleation
Operator (physics)
Orthogonal polynomials
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Partial differential equation
Partial fraction decomposition
Partition function (mathematics)
Partition function (statistical mechanics)
Permutation
Permutation matrix
Pfaffian
Poisson point process
Polynomial
Power series
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Probability
Probability density function
Probability measure
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Quaternion
Random matrix
Riemann sum
Riemann zeta function
Scaling limit
Scatter matrix
Schur polynomial
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Statistic
Statistical mechanics
Subsequence
Symmetric matrix
Symmetrization
Symplectic matrix
Trace formula
Tridiagonal matrix
Unitary matrix
Volume form
Product details
- ISBN 9780691128290
- Weight: 1729g
- Dimensions: 203 x 254mm
- Publication Date: 21 Jul 2010
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Hardback
- Language: English
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Random matrix theory, both as an application and as a theory, has evolved rapidly over the past fifteen years. Log-Gases and Random Matrices gives a comprehensive account of these developments, emphasizing log-gases as a physical picture and heuristic, as well as covering topics such as beta ensembles and Jack polynomials. Peter Forrester presents an encyclopedic development of log-gases and random matrices viewed as examples of integrable or exactly solvable systems. Forrester develops not only the application and theory of Gaussian and circular ensembles of classical random matrix theory, but also of the Laguerre and Jacobi ensembles, and their beta extensions. Prominence is given to the computation of a multitude of Jacobians; determinantal point processes and orthogonal polynomials of one variable; the Selberg integral, Jack polynomials, and generalized hypergeometric functions; Painleve transcendents; macroscopic electrostatistics and asymptotic formulas; nonintersecting paths and models in statistical mechanics; and applications of random matrix theory.
This is the first textbook development of both nonsymmetric and symmetric Jack polynomial theory, as well as the connection between Selberg integral theory and beta ensembles. The author provides hundreds of guided exercises and linked topics, making Log-Gases and Random Matrices an indispensable reference work, as well as a learning resource for all students and researchers in the field.
Peter J. Forrester is professor of mathematics at the University of Melbourne.
