Date of Award

1-1-2020

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Mathematics and Statistics

Content Description

1 online resource (vii, 48 pages) : illustrations.

Dissertation/Thesis Chair

Martin V Hildebrand

Committee Members

Karin Reinhold, Joshua Isralowitz

Keywords

bound order log(p)log(log p), convergence rate to uniform, Fibonary expansion, Fourier Transform, probability theory, random process, Fourier transformations, Fibonacci numbers, Transformations (Mathematics)

Subject Categories

Physical Sciences and Mathematics

Abstract

First, we examine the random process of the form Xn+1 = AXn + Bn (mod p) where A is a fixed 2x2 matrix with entries 2, 1, 1, 1, B_0, B_1, B_2,... are independent and identically distributed on the vectors [0 0], [0 1], [1 0], and X_0 is the 0 vector, with the goal of bounding the rate of convergence of this process to the uniform distribution.

Download

Share

COinS