Random walks on the torus with several generators

Details Random walks on the torus with several generators Random walks on the torus with several generators

Publishing date

2003-08-31

URL

arxiv.org/abs/math/0309011v2

Journals

Random Structures and Algorithms 25 (2004), 336-345.

Science

Mathematics

Field

Probability

Additional info

10 pages; related work at http://www.math.hmc.edu/~su/papers.html

Type

Scientific paper

Digital Object Identifier

10.1002/rsa.20029

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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