Search for dissertations about: "random matrices"

Showing result 1 - 5 of 47 swedish dissertations containing the words random matrices.

2. 1. Asymptotics of random matrices and matrix valued processes

   Author : Stefan Israelsson; Kurt Johansson; Uppsala universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; Mathematics; Random matrices; singular interaction; spectral distribution; fluctuation limit; distribution valued processes; MATEMATIK; MATHEMATICS; MATEMATIK; matematisk statistik; Mathematical Statistics;

   Abstract : This thesis contains three parts. In the first two papers we consider spectral properties of symmetric matrices with elements consisting of independent Ornstein Uhlenbeck processes. The eigenvalues behave as a particle system on the real line with singular interaction consisting of electrostatic repulsion and a linear restoring force. READ MORE

4. 2. Limit theorems for generalizations of GUE random matrices

   Author : Martin Bender; Kurt Johansson; Arno Kuijlaars; KTH; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; Random matrices; Central limit theorem; Dyson s Brownian motion; Interacting diffusion; Point process; Non-Hermitian; Scaling limit; MATHEMATICS; MATEMATIK;

   Abstract : This thesis consists of two papers devoted to the asymptotics of random matrix ensembles and measure valued stochastic processes which can be considered as generalizations of the Gaussian unitary ensemble (GUE) of Hermitian matrices H=A+A†, where the entries of A are independent identically distributed (iid) centered complex Gaussian random variables. In the first paper, a system of interacting diffusing particles on the real line is studied; special cases include the eigenvalue dynamics of matrix-valued Ornstein-Uhlenbeck processes (Dyson's Brownian motion). READ MORE

5. 3. Random Geometry and Reinforced Jump Processes

   Author : Tuan-Minh Nguyen; Probability and Inference Theory Group; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; random polygons; products of random matrices; vertex-reinforced jump processes; pseudotrajectories; random walks in simplexes; Markov chains in a general state space;

   Abstract : This thesis comprises three papers studying several mathematical models related to geometric Markov processes and random processes with reinforcements. The main goal of these works is to investigate the dynamics as well as the limiting behaviour of the models as time goes to infinity, the existence of invariant measures and limiting distributions, the speed of convergence and other interesting relevant properties. READ MORE

6. 4. Stochastic systems with locally defined dynamics

   Author : Anton Muratov; Göteborgs universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; point process; sequential adsorption; stopping set; random measure; Polya urn; convergence of empirical measures; bit flipping; recurrence; renewal process; Poisson process; Dirichlet distribution; random matrices; random matrices;

   Abstract : We study three different classes of models of stochastic systems with locally defined dynamics. Our main points of interest are the limiting properties and convergence in these models. The first class is the locally interactive sequential adsorption, or LISA, models. READ MORE

7. 5. Interlaced particles in tilings and random matrices

   Author : Eric Nordenstam; Kurt Johansson; Pierre van Moerbeke; KTH; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; Interlaced particles; GUE; Anti-symmetric GUE; domino tilings; lozenge tilings; Algebra; geometry and mathematical analysis; Algebra; geometri och analys;

   Abstract : This thesis consists of three articles all relatedin some way to eigenvalues of random matrices and theirprincipal minors and also to tilings of various planar regions with dominoes or rhombuses.Consider an $N\times N$ matrix $H_N=[h_{ij}]_{i,j=1}^N$ from the Gaussian unitary ensemble (GUE). READ MORE