An Exercise(?) in Fourier Analysis on the Heisenberg Group
An Exercise(?) in Fourier Analysis on the Heisenberg Group
Let H(n) be the group of 3×3 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 …