An Exercise (?) in Fourier Analysis on the Heisenberg Group (1502.04160v1)

Published 14 Feb 2015 in math.PR

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 n² 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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