Date of Award

1-1-2012

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Mathematics and Statistics

Content Description

1 online resource (v, 32 pages)

Dissertation/Thesis Chair

Martin V Hildebrand

Committee Members

Karin Reinhold-Larsson, Antun Milas, Carlos Rodriguez

Keywords

Finite fourier transform, Probability Theory, Random Process, Representation theory, Upper Bound Lemma, Variation Distance, Fourier transformations, Random number generators, Numbers, Random

Subject Categories

Physical Sciences and Mathematics

Abstract

A common way for computers to generate pseudo random number sequences is by using recurrences such as Xn+1=aXn+b (mod p) where a, b, and p are fixed integers. Even though this process generates pseudo random numbers it is completely determined by X0,a,b,p. Chung, Diaconis, and Graham, found bounds as p → infinity for the random process Xn+1=aXn+bn (mod p) where a is a fixed integer, and bn is either -1,0, or 1.

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