Victor Dubach

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math.PR2026

Limits of descent-biased trees

Victor Dubach, Paul Thévenin, Stephan Wagner

We investigate scaling and local limits of random trees biased according to their number of descents. A descent in a rooted labeled tree $t$ is a parent-child pair such that the la…

math.PR2026

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

Thomas Budzinski, Victor Dubach, Valentin Féray +2

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 conv…

math.PR2024

Classical patterns in Mallows permutations

Victor Dubach

We study classical pattern counts in Mallows random permutations with parameters $(n, q_{n})$ , as $n \to \infty$ . We focus on three different regimes for the parameter $q = q_{n}$ . When $…

math.PR2024

Binary search trees of permuton samples

Benoît Corsini, Victor Dubach, Valentin Féray

Binary search trees (BST) are a popular type of data structure when dealing with ordered data. Indeed, they enable one to access and modify data efficiently, with their height corr…

math.PR2024

A geometric approach to conjugation-invariant random permutations

Victor Dubach

We propose a new approach to conjugation-invariant random permutations. Namely, we explain how to construct uniform permutations in given conjugacy classes from certain point proce…

math.PR2023

Increasing subsequences of linear size in random permutations and the Robinson-Schensted tableaux of permutons

Victor Dubach

The study of longest increasing subsequences (LIS) in permutations led to that of Young diagrams via Robinson-Schensted's (RS) correspondence. In a celebrated paper, Vershik and Ke…