Asymptotic combinatorics with applications to mathematical physics : a European Mathematical Summer School held at the Euler Institute, St. Petersburg, Russia, July 9-20, 2001
Asymptotic combinatorics with applications to mathematical physics : a European Mathematical Summer School held at the Euler Institute, St. Petersburg, Russia, July 9-20, 2001
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发表时间：
2003
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通讯作者：
A. Vershik
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作者：
A. Vershik
随机矩阵，正交多项式和Riemann-Hilbert问题。-渐近表示理论和Riemann-Hilbert问题。-关于随机矩阵理论的四个讲座。-自由概率理论和随机矩阵。-代数几何，对称函数和调和分析。-对称群的Plancerel测度的Kerov高斯极限的非对易版本。-随机树和曲线的模。-无限对称群上的调和分析。-两堂关于杨图的渐近表示理论和统计的讲座。-III组合学和表示理论。-对称群和自由累积量的特征。-反射群的代数长度和庞加莱级数及其在表示理论中的应用。-退化精细Hecke代数的混合钩长公式。
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 Poincare series on reflection groups with applications to representations theory.- Mixed hook-length formula for degenerate a fine Hecke algebras.