2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61008We analyze the drunkard's walk on the unit sphere with step size theta and show that the walk converges in order constant/sin^2(theta) steps in the discrepancy metric. 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.20 pages; to appear in Electron. J. Probab.; related work at http://www.math.hmc.edu/~su/papers.htmlProbabilityRepresentation Theory60B15 (Primary) 43A85 (Secondary)text