On a Question of Chung, Diaconis, and Graham
نویسنده
چکیده
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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On the Chung-diaconis-graham Random Pro- Cess
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...
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