An elementary proof of anti-concentration of polynomials in Gaussian variables

Tridiagonal Realization of the Anti-symmetric Gaussian Β-ensemble

Abstract. The Householder reduction of a member of the anti-symmetric Gaussian unitary ensemble gives an anti-symmetric tridiagonal matrix with all independent elements. The random variables permit the introduction of a positive parameter β, and the eigenvalue probability density function of the corresponding random matrices can be computed explicitly, as can the distribution of {qi}, the first...

A New Type-2 Fuzzy Systems for Flexible-Joint Robot Arm Control

In this paper an adaptive neuro fuzzy inference system based on interval Gaussian type-2 fuzzy sets in the antecedent part and Gaussian type-1 fuzzy sets as coefficients of linear combination of input variables in the consequent part is presented. The capability of the proposed method (we named ANFIS2) to function approximation and dynamical system identification is shown. The ANFIS2 structure ...

An Identity of Jack Polynomials

In this work we give an alterative proof of one of basic properties of zonal polynomials and generalised it for Jack polynomials

Math 247a: Introduction to Random Matrix Theory

1. Wigner Matrices 2 2. Wigner’s Semicircle Law 4 3. Markov’s Inequality and Convergence of Expectation 6 4. First Proof of Wigner’s Semicircle Law 7 4.1. Convergence of matrix moments in Expectation 7 4.2. Convergence of Matrix Moments in Probability 12 4.3. Weak Convergence 15 5. Removing Moment Assumptions 17 6. Largest Eigenvalue 21 7. The Stiletjes Transform 31 8. The Stieltjes Transform a...

On the average number of sharp crossings of certain Gaussian random polynomials