Limit Profile for the Transpose Top-2 with Random Shuffle
Subhajit Ghosh, Nishu Kumari · SIAM Journal on Discrete Mathematics · 2025
Abstract. The transpose top-2 with random shuffle [S. Ghosh, J. Theoret. Probab., 33 (2020), pp. 1832–1854] is a lazy random walk on the alternating group [Formula: see text] generated by 3-cycles of the form [Formula: see text] and [Formula: see text]. We obtain the limit profile of this random walk by comparing it with the random walk on [Formula: see text] generated by all 3-cycles. Our method employs a noncommutative Fourier analysis analogue of the comparison method introduced by Nestoridi [ Electron. J. Probab., 29 (2024), 58, 14 pp.]. We also give the complete spectrum of alternating group graph, thus answering a question of Huang and Huang [ J. Algebraic Combin., 50 (2019), pp. 99–111].