Discrepancy Convergence for the Drunkard's Walk on the Sphere
Francis Edward Su, Harvey Mudd College
Abstract
We analyze the drunkard's walk on the unit sphere with step size
(theta) and show that the walk converges in order C/sin^2(theta)
steps in the discrepancy metric (C a constant).
This is an application of techniques we develop for
bounding the discrepancy of random walks on Gelfand pairs
generated by bi-invariant measures.
In such cases, Fourier analysis on the acting group
admits tractable computations involving spherical functions.
We advocate the use of discrepancy as a metric on probabilities
for state spaces with isometric group actions.
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