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arXiv · 1607.05716

Sums of twisted circulants

Aaron Abrams·Henry Landau·Zeph Landau·James Pommersheim
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Abstract

The rate of convergence of simple random walk on the Heisenberg group over $Z/nZ$ with a standard generating set was determined by Bump et al [1,2]. We extend this result to random walks on the same groups with an arbitrary minimal symmetric generating set. We also determine the rate of convergence of simple random walk on higher-dimensional versions of the Heisenberg group with a standard generating set. We obtain our results via Fourier analysis, using an eigenvalue bound for sums of twisted circulant matrices. The key tool is a generalization of a version of the Heisenberg Uncertainty Principle due to Donoho-Stark [4].

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Aaron Abrams, Henry Landau, Zeph Landau, James Pommersheim. 2016-07-19. Sums of twisted circulants. https://arxiv.org/abs/1607.05716

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