On the Chung-Diaconis-Graham random process
Probability
2007-08-20 v2
Abstract
Chung, Diaconis, and Graham considered random processes of the form X_{n+1}=2X_n+b_n (mod p) where X_0=0, p is odd, and b_n for n=0,1,2,... are i.i.d. random variables on {-1,0,1}. If Pr(b_n=-1)= Pr(b_n=1)=\beta and Pr(b_n=0)=1-2\beta, they asked which value of \beta makes X_n get close to uniformly distributed on the integers mod p the slowest. In this paper, we extend the results of Chung, Diaconis, and Graham in the case p=2^t-1 to show that for 0<\beta<=1/2, there is no such value of \beta.
Cite
@article{arxiv.math/0508427,
title = {On the Chung-Diaconis-Graham random process},
author = {Martin Hildebrand},
journal= {arXiv preprint arXiv:math/0508427},
year = {2007}
}
Comments
11 pages; This version corrects a flaw in the original version