Convergence of Random Walks on the Circle Generated by an Irrational Rotation

Abstract

Fix α ∈ [0, 1). Consider the random walk on the circle S1 which proceeds by repeatedly rotating points forward or backward, with probability 1 2 , by an angle 2πα. This paper analyzes the rate of convergence of this walk to the uniform distribution under “discrepancy” distance. The rate depends on the continued fraction properties of the number ξ = 2α. We… (More)

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Cite this paper

@inproceedings{Su1998ConvergenceOR, title={Convergence of Random Walks on the Circle Generated by an Irrational Rotation}, author={Francis Edward Su}, year={1998} }