מרצה/ים:
רון פלד
סיכומים:
Thursday, October 26, 2017
Thursday, October 26, 2017
נושאי השיעור:
- introduction and motivation
- the Wigner model
- method of moments
- moments of semi - circle law
Tuesday, October 31, 2017
נושאי השיעור:
- basic properties of Catalan numbers
- proof of Wigner's theorem
Tuesday, November 14, 2017
נושאי השיעור:
- proof of lemma from previous lesson
- generalization of the Wigner theorem to:
- complex Wigner matrices
- reducing the moment restriction
Tuesday, November 14, 2017
נושאי השיעור:
- theorem on maximal eigenvalue
- logarithmic Sobolev inequalities
- Herbst's lemma
- implication on random matrices
Sunday, November 26, 2017
נושאי השיעור:
- alternative approach to Wigner's theorem using Stieltjes transform
- relations with convergance of measures
Tuesday, November 28, 2017
נושאי השיעור:
- Gaussian Orthogonal/ Unitary ensemble
- density of GOE, GUE on matrices
- joint density of the eigenvalues
Tuesday, December 5, 2017
נושאי השיעור:
- Hermite polynomials - defintion and properties
- oscillator wave function
- formula for joint density of p unordered eigenvalues
- integration of these densities
- introduction of Fredholm determinants
- Gaudin - Mehta theorem
Tuesday, December 12, 2017
נושאי השיעור:
- Hadamard inequality
- continuity of Fredholm determinants
- additional properties of Hermite polynomials
- proof of main lemma - finishing the proof of the Gaudin - Mehta theorem
- Laplace method (Saddle point method) - idea
- Laplace theorem