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We theoretically analyze the properties of a geodesic random walk on theEuclidean $d$-sphere. Specifically, we prove that the random walk's transitionkernel is Wasserstein contractive with a contraction rate which can be boundedfrom above independently of the dimension $d$. Our result is of particularinterest due to its implications regarding the potential fordimension-independent performance of both geodesic slice sampling on the sphereand Gibbsian polar slice sampling, which are Markov chain Monte Carlo methodsfor approximate sampling from essentially arbitrary distributions on theirrespective state spaces.

A Dimension-Independent Bound on the Wasserstein Contraction Rate of a Geodesic Random Walk on the Sphere