## Asymptotic Combinatorics with Application to Mathematical PhysicsNew and striking results obtained in recent years from an intensive study of asymptotic combinatorics have led to a new, higher level of understanding of related problems: the theory of integrable systems, the Riemann-Hilbert problem, asymptotic representation theory, spectra of random matrices, combinatorics of Young diagrams and permutations, and even some aspects of quantum field theory. |

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### Contents

IV | 3 |

V | 23 |

VI | 51 |

VII | 71 |

VIII | 97 |

IX | 113 |

X | 151 |

XI | 167 |

XII | 209 |

XIII | 221 |

XIV | 245 |

XV | 255 |

XVI | 267 |

XVII | 279 |

XVIII | 307 |

### Other editions - View all

Asymptotic Combinatorics with Application to Mathematical Physics V.A. Malyshev,A.M. Vershik Limited preview - 2002 |

Asymptotic Combinatorics with Application to Mathematical Physics V.A. Malyshev,A.M. Vershik Limited preview - 2012 |

### Common terms and phrases

arbitrary Asymptotic Combinatorics basic hypergeometric series Berezin boson boundary Brownian Brownian bridge canonical coefficients Combinatorics component computation consider constant convergence correlation functions corresponding defined definition denote density diagrams distribution edges eigenvalues equation example fermionic Feynman finite fixed formula functional invariance principle given graphs Hamiltonian Hermitian idempotent integral Jacobi Jacobi matrix Kazakov Lemma Lie algebra Lie superalgebra limit linear Malyshev Math Mathematical Physics matrix model measure obtain operator p-adic p-mappings parabolic subgroup parameters partition function Phys planar polynomial potential problem proof quantization quantum random mappings random matrix random matrix theory random trees relation renormalization representation respect Riemann Riemann zeta function root sampling invariance principle satisfies Section semiring space string SU(N surface symmetric term Theorem theta hypergeometric series topology transformation triangulations unitary values variables vector vector bundle Vershik vertex vertices Yangian zero zeta function

### Popular passages

Page 265 - Mathematins can be treated as a result of a dequantization of the traditional Mathematics as the Planck constant tends to zero taking pure imaginary values. In the framework of Idempotent Mathematics some basic concepts and results of the theory of group representations (including some unexpected theorems of the Engel type) are discussed.