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arXiv · 2407.19878

Limit profile for the transpose top-2 with random shuffle

Subhajit Ghosh·Nishu Kumari
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Abstract

The transpose top-$2$ with random shuffle (J. Theoret. Probab., 2020) is a lazy random walk on the alternating group $A_n$ generated by $3$-cycles of the form $(\star,n-1,n)$ and $(\star,n,n-1)$. We obtain the limit profile of this random walk by comparing it with the random walk on $A_n$ generated by all $3$-cycles. Our method employs a non-commutative Fourier analysis analogue of the comparison method introduced by Nestoridi (Electron. J. Probab., 2024). We also give the complete spectrum of the alternating group graph, thus answering a question of Huang and Huang (J. Algebraic Combin., 2019).

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Subhajit Ghosh, Nishu Kumari. 2024-07-29. Limit profile for the transpose top-2 with random shuffle. https://doi.org/10.1137/24m1682245

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