Random walks on discrete and continuous circles

1 December 1993

journal article
Published by Cambridge University Press (CUP) in Journal of Applied Probability

Vol. 30 (4) , 780-789
https://doi.org/10.2307/3214512

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 S¹.

Keywords

DISCRETE
CONTINUOUS CIRCLE
FUNCTION
RANDOM WALKS
DIACONIS
MOTIVATED
STATIONARITY
CONVERGENCE

This publication has 1 reference indexed in Scilit:

Group representations in probability and statistics
Published by Institute of Mathematical Statistics ,1988