Limit profile for the transpose top-2 with random shuffle
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914073590890496 |
|---|---|
| author | Ghosh, Subhajit Kumari, Nishu |
| author_facet | Ghosh, Subhajit Kumari, Nishu |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19878 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Limit profile for the transpose top-2 with random shuffle Ghosh, Subhajit Kumari, Nishu Probability Combinatorics 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). |
| title | Limit profile for the transpose top-2 with random shuffle |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2407.19878 |