Title | Asymptotic Combinatorics with Applications to Mathematical Physics [electronic resource] : A European Mathematical Summer School held at the Euler Institute, St. Petersburg, Russia July 9-20, 2001 / edited by Anatoly M. Vershik, Yuri Yakubovich |
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Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 2003 |

Connect to | http://dx.doi.org/10.1007/3-540-44890-X |

Descript | X, 250 p. online resource |

SUMMARY

At the Summer School Saint Petersburg 2001, the main lecture courses bore on recent progress in asymptotic representation theory: those written up for this volume deal with the theory of representations of infinite symmetric groups, and groups of infinite matrices over finite fields; Riemann-Hilbert problem techniques applied to the study of spectra of random matrices and asymptotics of Young diagrams with Plancherel measure; the corresponding central limit theorems; the combinatorics of modular curves and random trees with application to QFT; free probability and random matrices, and Hecke algebras

CONTENT

Random matrices, orthogonal polynomials and Riemann โ{128}{148} Hilbert problem -- Asymptotic representation theory and Riemann โ{128}{148} Hilbert problem -- Four Lectures on Random Matrix Theory -- Free Probability Theory and Random Matrices -- Algebraic geometry,symmetric functions and harmonic analysis -- A Noncommutative Version of Kerovโ{128}{153}s Gaussian Limit for the Plancherel Measure of the Symmetric Group -- Random trees and moduli of curves -- An introduction to harmonic analysis on the infinite symmetric group -- Two lectures on the asymptotic representation theory and statistics of Young diagrams -- III Combinatorics and representation theory -- Characters of symmetric groups and free cumulants -- Algebraic length and Poincarรฉ series on reflection groups with applications to representations theory -- Mixed hook-length formula for degenerate a fine Hecke algebras

Mathematics
Group theory
Functional analysis
Partial differential equations
Applied mathematics
Engineering mathematics
Combinatorics
Physics
Mathematics
Applications of Mathematics
Physics general
Combinatorics
Group Theory and Generalizations
Functional Analysis
Partial Differential Equations