Extreme Values of Permutation Statistics
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866908382114349056 |
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| author | Dörr, Philip Kahle, Thomas |
| author_facet | Dörr, Philip Kahle, Thomas |
| contents | We investigate extreme values of Mahonian and Eulerian distributions arising from counting inversions and descents of random elements of finite Coxeter groups. To this end, we construct a triangular array of either distribution from a sequence of Coxeter groups with increasing ranks. To avoid degeneracy of extreme values, the number of i.i.d. samples $k_n$ in each row must be asymptotically bounded. We employ large deviations theory to prove the Gumbel attraction of Mahonian and Eulerian distributions. It is shown that for the two classes, different bounds on $k_n$ ensure this. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_01426 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Extreme Values of Permutation Statistics Dörr, Philip Kahle, Thomas Combinatorics Probability Primary: 60G70, 05A16, Secondary: 20F55, 62R01 We investigate extreme values of Mahonian and Eulerian distributions arising from counting inversions and descents of random elements of finite Coxeter groups. To this end, we construct a triangular array of either distribution from a sequence of Coxeter groups with increasing ranks. To avoid degeneracy of extreme values, the number of i.i.d. samples $k_n$ in each row must be asymptotically bounded. We employ large deviations theory to prove the Gumbel attraction of Mahonian and Eulerian distributions. It is shown that for the two classes, different bounds on $k_n$ ensure this. |
| title | Extreme Values of Permutation Statistics |
| topic | Combinatorics Probability Primary: 60G70, 05A16, Secondary: 20F55, 62R01 |
| url | https://arxiv.org/abs/2205.01426 |