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Random Walks On The Torus With Several Generators, Timothy Prescott '02, Francis E. Su

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Given n vectors {_i} ∈ [0, 1)^d, consider a random walk on the d-dimensional torus ^d = ℝ^d/ℤ^d generated by these vectors by successive addition and subtraction. For certain sets of vectors, this walk converges to Haar (uniform) measure on the torus. We show that the discrepancy distance D(Q*^k) between the kth step distribution of the walk and Haar measure is bounded below by D(Q*^k) ≥ C₁k^−n/2, where C₁ = C(n, d) is …