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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2504.07918 |
| Etiquetas: |
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- We consider a family of card shuffles of $n$ cards in which the allowed moves involve transpositions corresponding to the Jucys--Murphy elements of the symmetric group $\{S_m\}_{m \leq n}$. We determine the eigenvalues of the corresponding $n! \times n!$ transition matrices of these shuffles and study the mixing times for a special case, the $k$--star transpositions shuffle, a natural interpolation between the random transpositions shuffle, introduced and studied by Diaconis and Shahshahani, and the star transpositions shuffle, introduced and studied by Diaconis. We prove that the $k$--star transpositions shuffle exhibits total variation cutoff at $\frac{2n-(k+1)}{2(n-1)}n\log n$ with a window of $\frac{2n-(k+1)}{2(n-1)}n$. Furthermore, in the regimes $k/n \rightarrow 0$ or $k/n \rightarrow 1$, this shuffle has the same limit profile as random transpositions, which has been fully determined by Teyssier.