Sökning: "Central Limit Theorems"
Visar resultat 1 - 5 av 6 avhandlingar innehållade orden Central Limit Theorems.
1. Limit theorems for generalizations of GUE random matrices
Sammanfattning : 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). LÄS MER
2. Limit Theorems for Lattices and L-functions
Sammanfattning : This PhD thesis investigates distributional questions related to three types of objects: Unimodular lattices, symplectic lattices, and Hecke L-functions of imaginary quadratic number fields of class number 1. In Paper I, we follow Södergren and examine the asymptotic joint distribution of a collection of random variables arising as geometric attributes of the N = N(n) shortest non-zero lattice vectors (up to sign) in a random unimodular lattice in n-dimensional Euclidean space, as the dimension n tends to infinity: Normalizations of the lengths of these vectors, and normalizations of the angles between them. LÄS MER
3. Limit Theorems for Ergodic Group Actions and Random Walks
Sammanfattning : This thesis consists of an introduction, a summary and 7 papers. The papers are devoted to problems in ergodic theory, equidistribution on compact manifolds and random walks on groups. In Papers A and B, we generalize two classical ergodic theorems for actions of abelian groups. LÄS MER
4. On determinantal point processes and random tilings with doubly periodic weights
Sammanfattning : This thesis is dedicated to asymptotic analysis of determinantal point processes originating from random matrix theory and random tiling models. Our main interest lies in random tilings of planar domains with doubly periodic weights. LÄS MER
5. Markov Chains, Renewal, Branching and Coalescent Processes : Four Topics in Probability Theory
Sammanfattning : This thesis consists of four papers.In paper 1, we prove central limit theorems for Markov chains under (local) contraction conditions. As a corollary we obtain a central limit theorem for Markov chains associated with iterated function systems with contractive maps and place-dependent Dini-continuous probabilities. LÄS MER
