Large deviation principles for pattern-avoiding permutations, and limit shapes for constrained Mallows permutations
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915959481040896 |
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| author | Budzinski, Thomas Dubach, Victor Féray, Valentin Kammoun, Mohamed Slim Maïda, Mylène |
| author_facet | Budzinski, Thomas Dubach, Victor Féray, Valentin Kammoun, Mohamed Slim Maïda, Mylène |
| contents | We study Mallows random permutations conditioned to avoid a given pattern $α$ of length~$3$. When the bias parameter is of the form $e^{β/n}$, we prove that these permutations converge to a non-trivial explicit deterministic permuton that depends on the pattern $α$ and on the parameter $β$. Along the way, we provide parametrizations for $α$-avoiding permutons, and establish a large deviation principle for uniform $α$-avoiding permutations. As a byproduct of the proof, we also obtain asymptotic estimates of two versions of $q$-Catalan numbers in the regime $q=e^{β/n}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23751 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Large deviation principles for pattern-avoiding permutations, and limit shapes for constrained Mallows permutations Budzinski, Thomas Dubach, Victor Féray, Valentin Kammoun, Mohamed Slim Maïda, Mylène Probability Combinatorics 05A05, 05A19, 60C05, 60F10 We study Mallows random permutations conditioned to avoid a given pattern $α$ of length~$3$. When the bias parameter is of the form $e^{β/n}$, we prove that these permutations converge to a non-trivial explicit deterministic permuton that depends on the pattern $α$ and on the parameter $β$. Along the way, we provide parametrizations for $α$-avoiding permutons, and establish a large deviation principle for uniform $α$-avoiding permutations. As a byproduct of the proof, we also obtain asymptotic estimates of two versions of $q$-Catalan numbers in the regime $q=e^{β/n}$. |
| title | Large deviation principles for pattern-avoiding permutations, and limit shapes for constrained Mallows permutations |
| topic | Probability Combinatorics 05A05, 05A19, 60C05, 60F10 |
| url | https://arxiv.org/abs/2604.23751 |