A lower bound for the Chung-Diaconis-Graham random process
Abstract
Chung, Diaconis, and Graham considered random processes of the form Xn+1=an Xn+bn (mod p) where p is odd, X0=0, an=2 always, and bn are i.i.d. for n=0,1,2,... . In this paper, we show that if P(bn=-1)=Pbn=0)=P(bn=1)=1/3, then there exists a constant c>1 such that c log2 p steps are not enough to make Xn get close to uniformly distributed on the integers mod p.
0