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Limit profile for the transpose top-2 with random shuffle
- Publication Year :
- 2024
-
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).
- Subjects :
- Mathematics - Probability
Mathematics - Combinatorics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2407.19878
- Document Type :
- Working Paper