Essays about: "Gaussian ensembles"

Found 3 essays containing the words Gaussian ensembles.

  1. 1. Gap Probabilities in Random Matrix Ensembles

    University essay from Uppsala universitet/Analys och partiella differentialekvationer

    Author : Oskar Bäcklin; [2023]
    Keywords : gap probability; random matrix;

    Abstract : In this degree project we look at eigenvalue statistics of two randommatrix ensembles, the Gaussian and the circular ensembles. We beginwith their definition and discuss the joint probability distribution of theirentries and eigenvalues. READ MORE

  3. 2. Asymptotics of beta-Hermite Ensembles

    University essay from Linköpings universitet/Matematisk statistik; Linköpings universitet/Tekniska fakulteten

    Author : Filip Berglund; [2020]
    Keywords : beta-Hermite ensembles; Gaussian ensembles; empirical distribution function; level density; largest eigenvalue; order statistic; Sturm sequence; Hermite polynomials; beta-Hermite ensemblerna; gaussiska ensemblerna; empiriska fördelningsfunktionen; nivåtäthet; största egenvärdet; ordningsstatiska; Sturmföljder; Hermitepolynom;

    Abstract : In this thesis we present results about some eigenvalue statistics of the beta-Hermite ensembles, both in the classical cases corresponding to beta = 1, 2, 4, that is the Gaussian orthogonal ensemble (consisting of real symmetric matrices), the Gaussian unitary ensemble (consisting of complex Hermitian matrices) and the Gaussian symplectic ensembles (consisting of quaternionic self-dual matrices) respectively. We also look at the less explored general beta-Hermite ensembles (consisting of real tridiagonal symmetric matrices). READ MORE

  4. 3. A Review of Gaussian Random Matrices

    University essay from Linköpings universitet/Matematisk statistik; Linköpings universitet/Tekniska fakulteten

    Author : Kasper Andersson; [2020]
    Keywords : Random Matrix Theory; Gaussian Ensembles; Covariance; Wishart Ensembles; PCA; Neural Networks; Slumpmatristeori; Gaussian Ensembles; Kovarians; Wishart Ensembles; PCA; Neuronnät;

    Abstract : While many university students get introduced to the concept of statistics early in their education, random matrix theory (RMT) usually first arises (if at all) in graduate level classes. This thesis serves as a friendly introduction to RMT, which is the study of matrices with entries following some probability distribution. READ MORE