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Random walks on discrete and continuous circles

Published online by Cambridge University Press:  14 July 2016

Jeffrey S. Rosenthal
Jeffrey S. Rosenthal*
Affiliation:
University of Minnesota
*
∗ Postal address: School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA.
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Abstract

We consider a large class of random walks on the discrete circle Z/(n), defined in terms of a piecewise Lipschitz function, and motivated by the ‘generation gap' process of Diaconis. For such walks, we show that the time until convergence to stationarity is bounded independently of n. Our techniques involve Fourier analysis and a comparison of the random walks on Z/(n) with a random walk on the continuous circle S 1.

Keywords

FOURIER ANALYSISTIME TO STATIONARITYGENERATION GAP

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 4 , December 1993, pp. 780 - 789
Copyright
Copyright © Applied Probability Trust 1993 

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References

Diaconis, P. (1988) Group Representations in Probability and Statistics. IMS Lecture Series Volume 11, Institute of Mathematical Statistics, Hayward, California.Google Scholar
Dou, C. C. (1991) Enumeration and random walks on groups. Preprint.Google Scholar
Hildebrand, M. V. (1990) Rates of Convergence of Some Random Processes on Finite Groups. Ph.D. dissertation, Mathematics Department, Harvard University.Google Scholar
Kawata, T. (1972) Fourier Analysis in Probability Theory. Academic Press, New York.Google Scholar