An Exercise (?) in Fourier Analysis on the Heisenberg Group
Probability
2015-02-17 v1
Abstract
Let H(n) be the group of 3x3 uni-uppertriangular matrices with entries in Z/nZ, the integers mod n. We show that the simple random walk converges to the uniform distribution in order n^2 steps. The argument uses Fourier analysis and is surprisingly challenging. It introduces novel techniques for bounding the spectrum which are useful for a variety of walks on a variety of groups.
Cite
@article{arxiv.1502.04160,
title = {An Exercise (?) in Fourier Analysis on the Heisenberg Group},
author = {Daniel Bump and Persi Diaconis and Angela Hicks and Laurent Miclo and Harold Widom},
journal= {arXiv preprint arXiv:1502.04160},
year = {2015}
}
Comments
24 pages, 6 figures