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arXiv · 2604.23751

Large deviation principles for pattern-avoiding permutations, and limit shapes for constrained Mallows permutations

Thomas Budzinski·Victor Dubach·Valentin Féray·Mohamed Slim Kammoun·Mylène Maïda
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Abstract

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 $q=e^{β/n}$.

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Thomas Budzinski, Victor Dubach, Valentin Féray, Mohamed Slim Kammoun, Mylène Maïda. 2026-04-26. Large deviation principles for pattern-avoiding permutations, and limit shapes for constrained Mallows permutations. https://arxiv.org/abs/2604.23751

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