## Log-Gases and Random Matrices (LMS-34)Random matrix theory, both as an application and as a theory, has evolved rapidly over the past fifteen years. 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; Painlevé 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 |

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### Contents

1 | |

Chapter 2 Circular ensembles | 53 |

Chapter 3 Laguerre and Jacobi ensembles | 85 |

Chapter 4 The Selberg integral | 133 |

Chapter 5 Correlation functions at 946 2 | 186 |

Chapter 6 Correlation functions at 946 1 and 4 | 236 |

Chapter 7 Scaled limits at 946 1 2 and 4 | 283 |

Chapter 8 Eigenvalue probabilities Painlevé systems approach | 328 |

Chapter 10 Lattice paths and growth models | 440 |

Chapter 11 The CalogeroSutherland model | 505 |

Chapter 12 Jack polynomials | 543 |

Chapter 13 Correlations for general 946 | 592 |

Chapter 14 Fluctuation formulas and universal behavior of correlations | 658 |

Chapter 15 The twodimensional onecomponent plasma | 701 |

Bibliography | 765 |

785 | |