Abstract
In this paper, we investigate the properties of a random walk on the alternating group \(A_n\) generated by three cycles of the form \((i,n-1,n)\) and \((i,n,n-1)\). We call this the transpose top-2 with random shuffle. We find the spectrum of the transition matrix of this shuffle. We show that the mixing time is of order \(\left( n-\frac{3}{2}\right) \log n\) and prove that there is a total variation cutoff for this shuffle.
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Acknowledgements
I would like to thank my advisor Arvind Ayyer for fruitful conversations and suggestions in the preparation of this paper. I would also like to thank Amritanshu Prasad, Arvind Ayyer and Pooja Singla for proposing the problem. I am also thankful to all the reviewers for the careful reading of the manuscript and their valuable comments. I would like to acknowledge support in part by a UGC Centre for Advanced Study Grant.
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Ghosh, S. Total Variation Cutoff for the Transpose Top-2 with Random Shuffle. J Theor Probab 33, 1832–1854 (2020). https://doi.org/10.1007/s10959-019-00945-6
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DOI: https://doi.org/10.1007/s10959-019-00945-6