Permuton limit of a generalization of the Mallows and $k$-card-minimum models
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909510254198784 |
|---|---|
| author | Jasińska, Joanna Ráth, Balázs |
| author_facet | Jasińska, Joanna Ráth, Balázs |
| contents | We introduce and study a new random permutation model that generalizes the $k$-card minimum model defined by Travers and the Mallows model. We calculate the permuton limit of such a sequence of random permutations. As a corollary, we deduce the law of large numbers for pattern densities. Moreover, we prove a universality result about the band structure of the limiting permuton, confirming a conjecture of Travers about the $k$-card minimum model. More specifically, we show that if a certain model parameter goes to infinity then the appropriately scaled restriction of the permuton measure to a line that intersects the diagonal perpendicularly converges weakly to the logistic distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07258 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Permuton limit of a generalization of the Mallows and $k$-card-minimum models Jasińska, Joanna Ráth, Balázs Probability 60G42, 60J10, 60G42 We introduce and study a new random permutation model that generalizes the $k$-card minimum model defined by Travers and the Mallows model. We calculate the permuton limit of such a sequence of random permutations. As a corollary, we deduce the law of large numbers for pattern densities. Moreover, we prove a universality result about the band structure of the limiting permuton, confirming a conjecture of Travers about the $k$-card minimum model. More specifically, we show that if a certain model parameter goes to infinity then the appropriately scaled restriction of the permuton measure to a line that intersects the diagonal perpendicularly converges weakly to the logistic distribution. |
| title | Permuton limit of a generalization of the Mallows and $k$-card-minimum models |
| topic | Probability 60G42, 60J10, 60G42 |
| url | https://arxiv.org/abs/2412.07258 |