Limit profile for the transpose top-2 with random shuffle

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).

29 pages

References in corpus (5)

• The cutoff profile for the simple exclusion process on the circle
• Limit Profiles for Reversible Markov Chains
• The second largest eigenvalues of some Cayley graphs on alternating groups
• Total variation cutoff for the transpose top-$2$ with random shuffle
• Limit Profile for Projections of Random Walks on Groups