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Random walks on the torus with several generators

Timothy Prescott·Francis Edward Su
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Abstract

Our paper gives bounds for the rate of convergence for a class of random walks on the d-dimensional torus generated by a set of n vectors in R^d/Z^d. We give bounds on the discrepancy distance from Haar measure; our lower bound holds for all such walks, and if the generators arise from the rows of a "badly approximable" matrix, then there is a corresponding upper bound. The bounds are sharp for walks on the circle.

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Timothy Prescott, Francis Edward Su. 2004-04-27. Random walks on the torus with several generators. https://doi.org/10.1002/rsa.20029

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