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A Random Walk on the Heisenberg Group

Algebra & Discrete Mathematics

Speaker: Angela Hicks, Stanford Univ.
Location: 1147 MSB
Start time: Mon, May 2 2016, 4:10PM

The Heisenberg Group mod p is a particularly simple to describe noncommutative group. Analysis of a random walk on the group dates back to Zach, who was considering the effectiveness of certain random number generators. We'll discuss joint work with Daniel Bump, Persi Diaconis, Laurent Miclo, and Harold Widom that looks at analysing the walk using the Fourier analysis of groups, with an emphasis on how calculations on the irreducible representations of a group can be used to bound convergence of a walk to uniform. We'll assume some knowledge of linear algebra and a bit of basic group theory, but otherwise aim for an elementary talk.