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 Electronic Journal of Probability > Vol. 6 (2001) > Paper 2 open journal systems 


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.


Full text: PDF

Pages: 1-20

Published on: February 19, 2001
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Electronic Journal of Probability. ISSN: 1083-6489