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.
References
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This paper is based on parts of the author's doctoral dissertation written at The Johns Hopkins University
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Porod, U. L 2-lower bounds for a special class of random walks. Probab. Th. Rel. Fields 101, 277–289 (1995). https://doi.org/10.1007/BF01375829
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DOI: https://doi.org/10.1007/BF01375829
Mathematics Subject Classification
- 60J15
- 60B15
- 43A80