Poisson approximation for large permutation groups
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908338728468480 |
|---|---|
| author | Diaconis, Persi Tung, Nathan |
| author_facet | Diaconis, Persi Tung, Nathan |
| contents | Let $G_{k,n}$ be a group of permutations of $kn$ objects which permutes things independently in disjoint blocks of size $k$ and then permutes the blocks. We investigate the probabilistic and/or enumerative aspects of random elements of $G_{k,n}$. This includes novel limit theorems for fixed points, cycles of various lengths, number of cycles and inversions. The limits are compound Poisson distributions with interesting dependence structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06611 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Poisson approximation for large permutation groups Diaconis, Persi Tung, Nathan Probability Combinatorics Let $G_{k,n}$ be a group of permutations of $kn$ objects which permutes things independently in disjoint blocks of size $k$ and then permutes the blocks. We investigate the probabilistic and/or enumerative aspects of random elements of $G_{k,n}$. This includes novel limit theorems for fixed points, cycles of various lengths, number of cycles and inversions. The limits are compound Poisson distributions with interesting dependence structure. |
| title | Poisson approximation for large permutation groups |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2408.06611 |