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arXiv · 1502.04160

An Exercise (?) in Fourier Analysis on the Heisenberg Group

Daniel Bump·Persi Diaconis·Angela Hicks·Laurent Miclo·Harold Widom
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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.

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Daniel Bump, Persi Diaconis, Angela Hicks, Laurent Miclo, Harold Widom. 2015-02-14. An Exercise (?) in Fourier Analysis on the Heisenberg Group. https://arxiv.org/abs/1502.04160

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