The Sk shuffle block dynamics
- We introduce and analyze the S_k shuffle on N cards, a natural generalization of the celebrated random adjacent transposition shuffle. In the S_k shuffle, we choose uniformly at random a block of k consecutive cards, and shuffle these cards according to a permutation chosen uniformly at random from the symmetric group on k elements. We study the total-variation mixing time of the S_k shuffle when the number of cards N goes to infinity, allowing also k=k(N) to grow with N. In particular, we show that the cutoff phenomenon occurs when k=o(N^{\frac{1}{6}}).
| Author: | Evita Nestoridi, Amanda Priestley, Dominik SchmidGND |
|---|---|
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/123092 |
| URL: | https://alea.impa.br/english/index_v21.htm |
| ISSN: | 1980-0436OPAC |
| Parent Title (English): | ALEA - Latin American Journal of Probability and Mathematical Statistics |
| Publisher: | Institute for Applied and Pure Mathematics (IMPA) |
| Place of publication: | Rio de Janeiro |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2024 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2025/06/26 |
| Volume: | 21 |
| Issue: | 2 |
| First Page: | 1547 |
| Last Page: | 1566 |
| DOI: | https://doi.org/10.30757/alea.v21-58 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Stochastik und ihre Anwendungen | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
