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On the Chung-Diaconis-Graham random process


 
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1. Title Title of document On the Chung-Diaconis-Graham random process
 
2. Creator Author's name, affiliation, country Martin V. Hildebrand; University at Albany, SUNY
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random processes, discrete Fourier analysis
 
3. Subject Subject classification 60B15, 60J10
 
4. Description Abstract Chung, Diaconis, and Graham considered random processes of the form $X_{n+1}=2X_n+b_n \pmod p$ where $X_0=0$, $p$ is odd, and $b_n$ for $n=0,1,2,\dots$ 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 $0<\beta\le 1/2$, there is no such value of $\beta$.
 
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7. Date (YYYY-MM-DD) 2006-12-15
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1237
 
10. Identifier Digital Object Identifier 10.1214/ECP.v11-1237
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 11
 
12. Language English=en
 
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