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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2411.06006 |
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Table des matières:
- We prove a theorem that reduces bounding the mixing time of a card shuffle to verifying a condition that involves only triplets of cards. Then we use it to analyze a classic model of card shuffling. In 1988, Diaconis introduced the following Markov chain. Cards are arranged in an $n$ by $n$ grid. Each step, choose a row or column, uniformly at random, and cyclically rotate it by one unit in a random direction. He conjectured that the mixing time is ${\rm O}(n^3 \log n)$. We obtain a bound that is within a poly log factor of the conjecture.