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Record Nr. |
UNINA9910146272903321 |
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Titolo |
Asymptotic Combinatorics with Applications to Mathematical Physics : A European Mathematical Summer School held at the Euler Institute, St. Petersburg, Russia, July 9-20, 2001 / / edited by Anatoly M. Vershik |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2003 |
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ISBN |
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Edizione |
[1st ed. 2003.] |
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Descrizione fisica |
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1 online resource (X, 250 p.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 1815 |
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Disciplina |
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Soggetti |
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Applied mathematics |
Engineering mathematics |
Physics |
Combinatorics |
Group theory |
Functional analysis |
Partial differential equations |
Applications of Mathematics |
Physics, general |
Group Theory and Generalizations |
Functional Analysis |
Partial Differential Equations |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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Random matrices, orthogonal polynomials and Riemann — Hilbert problem -- Asymptotic representation theory and Riemann — 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 Kerov’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 |
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the asymptotic representation theory and statistics of Young diagrams -- III Combinatorics and representation theory -- Characters of symmetric groups and free cumulants -- Algebraic length and Poincaré series on reflection groups with applications to representations theory -- Mixed hook-length formula for degenerate a fine Hecke algebras. |
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Sommario/riassunto |
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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. |
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