L2-lower bounds for a special class of random walks
We investigate theL2-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 anL2-density. Our method uses work by Heckman on the asymptotics of multiplicities along a ray of representations. Several examples are presented.
Mathematics Subject Classification60J15 60B15 43A80
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