Total Variation Cutoff for the Transpose Top-2 with Random Shuffle

Subhajit Ghosh ()
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Subhajit Ghosh: Indian Institute of Science

Journal of Theoretical Probability, 2020, vol. 33, issue 4, 1832-1854

Abstract: Abstract In this paper, we investigate the properties of a random walk on the alternating group $$A_n$$ A n generated by three cycles of the form $$(i,n-1,n)$$ ( i , n - 1 , n ) and $$(i,n,n-1)$$ ( 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 $$\left( n-\frac{3}{2}\right) \log n$$ n - 3 2 log n and prove that there is a total variation cutoff for this shuffle.

Keywords: Random walk; Alternating group; Mixing time; Cutoff; Jucys–Murphy elements; 60J10; 60B15; 60C05 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10959-019-00945-6

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