Asymptotic Combinatorics with Applications to Mathematical Physics
Asymptotic Combinatorics with Applications to Mathematical Physics A European Mathematical Summer School held at the Euler Institute, St. Petersburg, Russia July 9–20, 2001 / [electronic resource] :
edited by Anatoly M. Vershik, Yuri Yakubovich.
- X, 250 p. online resource.
- Lecture Notes in Mathematics, 1815 0075-8434 ; .
- Lecture Notes in Mathematics, 1815 .
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 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.
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.
9783540448907
10.1007/3-540-44890-X doi
Mathematics.
Physics.
Combinatorics.
Group theory.
Functional analysis.
Differential equations, partial.
Applications of Mathematics.
Physics, general.
Combinatorics.
Group Theory and Generalizations.
Functional Analysis.
Partial Differential Equations.
T57-57.97
519
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 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.
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.
9783540448907
10.1007/3-540-44890-X doi
Mathematics.
Physics.
Combinatorics.
Group theory.
Functional analysis.
Differential equations, partial.
Applications of Mathematics.
Physics, general.
Combinatorics.
Group Theory and Generalizations.
Functional Analysis.
Partial Differential Equations.
T57-57.97
519