Sums of twisted circulants

2016/07/19 by Abrams, Aaron, Landau, Henry, Landau, Zeph +1
#60B15 #FOS: Mathematics #Group Theory (math.GR) #Probability (math.PR)

paper · doi:10.48550/arxiv.1607.05716

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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