Random permutations from $q$-Demazure products
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918433328726016 |
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| author | Tikhonov, Mikhail |
| author_facet | Tikhonov, Mikhail |
| contents | We study the $q$-deformation of the Demazure product model from arXiv:2407.21653. Consider the longest element $w_0$ in $S_n$ written as a reduced word in simple transpositions. Independently delete each transposition with probability $1-p$ and apply the $q$-Demazure product to the remaining ones. We show that the law of the resulting permutation converges as $n \to \infty$ to a deterministic permuton, which coincides with the $q=0$ case studied in arXiv:2407.21653 for adjusted probability $p'=p(1-q)/(1-qp)$. This resolves Conjecture 1.13 from arXiv:2407.21653 and identifies the limiting permuton explicitly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06532 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Random permutations from $q$-Demazure products Tikhonov, Mikhail Probability Combinatorics We study the $q$-deformation of the Demazure product model from arXiv:2407.21653. Consider the longest element $w_0$ in $S_n$ written as a reduced word in simple transpositions. Independently delete each transposition with probability $1-p$ and apply the $q$-Demazure product to the remaining ones. We show that the law of the resulting permutation converges as $n \to \infty$ to a deterministic permuton, which coincides with the $q=0$ case studied in arXiv:2407.21653 for adjusted probability $p'=p(1-q)/(1-qp)$. This resolves Conjecture 1.13 from arXiv:2407.21653 and identifies the limiting permuton explicitly. |
| title | Random permutations from $q$-Demazure products |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2604.06532 |