Essays about: "largest eigenvalues"

Found 3 essays containing the words largest eigenvalues.

  1. 1. 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

  3. 2. Limiting Behavior of the Largest Eigenvalues of Random Toeplitz Matrices

    University essay from KTH/Matematik (Inst.)

    Author : Samuel Modée; [2019]
    Keywords : Random matrix; Toeplitz matrix; largest eigenvalues; eigenvectors; slumpmatriser; Toeplitz matrices; största egenvärde; egenvektorer;

    Abstract : We consider random symmetric Toeplitz matrices of size n. Assuming that the entries on the diagonals are independent centered random variables with finite γ-th moment (γ>2), a law of large numbers is established for the largest eigenvalue. READ MORE

  4. 3. Return Models and Covariance Matrices

    University essay from Lunds universitet/Fysiska institutionen; Lunds universitet/Matematisk fysik

    Author : Xiaolei Xie; [2014]
    Keywords : returns; stochastic volatility; GARCH; covariance matrix; random matrix; spectral distribution; Physics and Astronomy;

    Abstract : Return models and covariance matrices of return series have been studied. In particular, GARCH and SV models are compared with respect to their forecasting accuracy when applied to intraday return series. SV models are found to be considerably more accurate and more consistent in accuracy in forecasting. READ MORE