Naumov, Alexey: Universality of some models of random matrices and random processes. 2012
Inhalt
- Introduction
- Universality in random matrix theory
- Universality in the strong law of large numbers
- Structure of thesis
- Notations
- Elliptic law for random matrices
- Main result
- Gaussian case
- Proof of the main result
- Least singular value
- Uniform integrability of logarithm
- Convergence of singular values
- Lindeberg's universality principe
- Some technical lemmas
- Semicircle law for a class of random matrices with dependent entries
- Strong law of large numbers for random processes
- Extension of the Brunk–Prokhorov theorem
- Strong law of large numbers for martingales with continuous parameter
- Analogues of the Kolmogorov and Prokhorov-Chow theorems for martingales
- The strong law of large numbers for homogeneous random processes with independent increments
- Some results from probability and linear algebra
- Methods
- Stochastic processes
- Bibliography