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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.07597 |
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| _version_ | 1866916283465859072 |
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| author | Sun, Maxwell |
| author_facet | Sun, Maxwell |
| contents | The Mallows distribution is a non-uniform distribution, first introduced over permutations to study non-ranked data, in which permutations are weighted according to their length. It can be generalized to any Coxeter group, and we study the distribution of $\text{des}(w) + \text{des}(w^{-1})$ where $w$ is a Mallows distributed element of a finite irreducible Coxeter group. We show that the asymptotic behavior of this statistic is Guassian. The proof uses a size-bias coupling with Stein's method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07597 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Central Limit Theorem on Two-Sided Descents of Mallows Distributed Elements of Finite Coxeter Groups Sun, Maxwell Combinatorics Probability The Mallows distribution is a non-uniform distribution, first introduced over permutations to study non-ranked data, in which permutations are weighted according to their length. It can be generalized to any Coxeter group, and we study the distribution of $\text{des}(w) + \text{des}(w^{-1})$ where $w$ is a Mallows distributed element of a finite irreducible Coxeter group. We show that the asymptotic behavior of this statistic is Guassian. The proof uses a size-bias coupling with Stein's method. |
| title | A Central Limit Theorem on Two-Sided Descents of Mallows Distributed Elements of Finite Coxeter Groups |
| topic | Combinatorics Probability |
| url | https://arxiv.org/abs/2406.07597 |