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Discrepancy Convergence for the Drunkard's Walk on the Sphere

   
@article{EJP75,
	author = {Francis Su},
	title = {Discrepancy Convergence for the Drunkard's Walk on the Sphere},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {6},
	year = {2001},
	keywords = {discrepancy, random walk, Gelfand pairs, homogeneous spaces, Legendre polynomials},
	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.},
	pages = {no. 2, 1-20},
	issn = {1083-6489},
	doi = {10.1214/EJP.v6-75},    
        url = {http://ejp.ejpecp.org/article/view/75}}