Log-Gases and Random Matrices (LMS-34) (eBook)

Peter J. Forrester (Autor)

eBook Download: PDF

2010
Princeton University Press (Verlag)
978-1-4008-3541-6 (ISBN)

Infos

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.

Autor

Peter J. Forrester is professor of mathematics at the University of Melbourne.

Produkt-Details

• Erscheint lt. Verlag: 1.7.2010
• Reihe/Serie: London Mathematical Society Monographs
• Reihe/Serie: London Mathematical Society Monographs
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Technik
• Schlagworte: asymptotic formula • Bidiagonal matrix • bijection • Binomial coefficient • Boltzmann distribution • Calculation • central limit theorem • Change of variables • Characteristic Polynomial • Charge Density • Circular ensemble • coefficient • complex number • Convergence of random variables • Correlation function • Correlation function (quantum field theory) • Correspondence principle • Cumulative distribution function • Degeneracy (mathematics) • Determinant • Diagram (category theory) • differential equation • Dirac equation • Dirac Operator • Dirichlet character • Doubly periodic function • Eigenfunction • Eigenvalues and Eigenvectors • elliptic function • Equation • Euler's formula • Explicit formulae (L-function) • factorial • Factorization • Fredholm determinant • gamma function • generalized Riemann hypothesis • geometric distribution • Haar measure • Harmonic oscillator • Hecke algebra • Hermite Polynomials • Hermitian matrix • hessenberg matrix • hypergeometric function • Integer lattice • Integer matrix • integral equation • Jacobi polynomials • Joint probability distribution • Laplace's equation • Lattice Path • Lie algebra • Mathematical Statistics • Minor (linear algebra) • nucleation • Operator (physics) • orthogonal polynomials • partial differential equation • Partial fraction decomposition • Partition function (mathematics) • Partition function (statistical mechanics) • Permutation • Permutation Matrix • Pfaffian • Poisson distribution • Poisson Point Process • polynomial • power series • Probability • Probability density function • Probability Distribution • probability measure • Proportionality (mathematics) • quantum entanglement • quaternion • random matrix • Riemann sum • Riemann zeta function • scaling limit • scatter matrix • Schur polynomial • Sign (mathematics) • singular value decomposition • Statistic • Statistical Mechanics • subsequence • symmetric function • Symmetric matrix • symmetrization • Symplectic Group • Symplectic matrix • theory • trace formula • transformation matrix • Trapezoidal rule • tridiagonal matrix • Unitary matrix • Variable (mathematics) • Volume form
• ISBN-10: 1-4008-3541-0 / 1400835410
• ISBN-13: 978-1-4008-3541-6 / 9781400835416