, Volume 101, Issue 2, pp 277-289

L 2-lower bounds for a special class of random walks

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Summary

We investigate theL 2-speed of convergence to stationarity for a certain class of random walks on a compact connected Lie group. We give a lower bound on the number of stepsk necessary such that thek-fold convolution power of the original step distribution has anL 2-density. Our method uses work by Heckman on the asymptotics of multiplicities along a ray of representations. Several examples are presented.

This paper is based on parts of the author's doctoral dissertation written at The Johns Hopkins University