Date of Award

1-1-2011

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, 44 pages)

Dissertation/Thesis Chair

Martin Hildebrand

Committee Members

Karin Reinhold, Carlos Rodriguez, Antun Milas

Keywords

bound, Diaconis, Hildebrand, lower, random, walk, Stochastic processes, Random walks (Mathematics)

Subject Categories

Mathematics | Physical Sciences and Mathematics

Abstract

Chung, Diaconis, and Graham considered random processes of the form X_(n+1)=(a_n)X_n+b_n (mod p) where p is odd, X_0=0, b_n are i.i.d. for n=0,1,2,... with P(b_n=0)=P(b_n=1)=P(b_n=-1)=1/3, and a_n=2 always. Later, Hildebrand was able to establish a lower bound for this process as p approaches infinity. This paper will prove the following conclusions on lower bounds of the Chung-Diaconis-Graham random process:

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