On a lower bound for the Chung–Diaconis–Graham random process

Martin Hildebrand

Statistics & Probability Letters, 2019, vol. 152, issue C, 121-125

Abstract: Consider the random process on the integers mod p with X0=0 and Xn+1=2Xn+bn(modp) where b0,b1,b2,… are i.i.d. random variables which can have only 1, 0, and −1 as possible values. We show that unless P(bn=0)=1∕2 or P(bn=1)=P(bn=−1)=1∕2, then for some C>1 depending on the probability distribution for bn, at least Clog2p steps are needed to make Xn close to uniformly distributed.

Keywords: Chung–Diaconis–Graham random process; Lower bound (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2019.04.020

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