On the Chung-Diaconis-Graham random process
Martin V. Hildebrand, University at Albany, SUNY
Abstract
Chung, Diaconis, and Graham considered random processes of the form
Xn+1=2Xn+bn (mod p) where
X0=0, p is odd, and bn for n=0, 1, 2, ... are
i.i.d. random variables on {-1,0,1}. If
Pr(bn=-1)=Pr(bn=1)=
β and Pr(bn=0)=1-2β, they asked which value of β
makes Xn 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=2t-1 to show that for
0<β≤1/2, there is no such value of β.
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