Random walks on the torus with several generators
概率论
2007-05-23 v2
摘要
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.
引用
@article{arxiv.math/0309011,
title = {Random walks on the torus with several generators},
author = {Timothy Prescott and Francis Edward Su},
journal= {arXiv preprint arXiv:math/0309011},
year = {2007}
}
备注
10 pages; related work at http://www.math.hmc.edu/~su/papers.html