Related papers: Square permutations are typically rectangular
We consider the random deposition of objects of variable width and height over a line. The successive additions of these structures create a random interface. We focus on the regime of heavy tailed distributions of the structure width. When…
Starting with a collection of $n$ oriented polygonal discs, with an even number $N$ of sides in total, we generate a random oriented surface by randomly matching the sides of discs and properly gluing them together. Encoding the surface in…
Spatial random permutations were originally studied due to their connections to Bose-Einstein condensation, but they possess many interesting properties of their own. For random permutations of a regular lattice with periodic boundary…
We study proportions of consecutive occurrences of permutations of a given size. Specifically, the feasible limits of such proportions on large permutations form a region, called feasible region. We show that this feasible region is a…
We consider uniform random permutations of length $n$ conditioned to have no cycle longer than $n^\beta$ with $0<\beta<1$, in the limit of large $n$. Since in unconstrained uniform random permutations most of the indices are in cycles of…
The Brownian separable permuton is a random probability measure on the unit square, which was introduced by Bassino, Bouvel, F\'eray, Gerin, Pierrot (2016) as the scaling limit of the diagram of the uniform separable permutation as size…
We study the number of occurrences of any fixed vincular permutation pattern. We show that this statistics on uniform random permutations is asymptotically normal and describe the speed of convergence. To prove this central limit theorem,…
The objects of our interest are the so-called $A$-permutations, which are permutations whose cycle length lie in a fixed set $A$. They have been extensively studied with respect to the uniform or the Ewens measure. In this paper, we extend…
Suppose we choose a permutation $\pi$ uniformly at random from $S_n$. Let $\mathsf{runsort}(\pi)$ be the permutation obtained by sorting the ascending runs of $\pi$ into lexicographic order. Alexandersson and Nabawanda recently asked if the…
We prove that the number of copies of any given permutation pattern $q$ has an asymptotically normal distribution in random permutations.
We introduce and study the writhe of a permutation, a circular variant of the well-known inversion number. This simple permutation statistics has several interpretations, which lead to some interesting properties. For a permutation sampled…
The classes of tree permutations and forest permutations were defined by Acan and Hitczenko (2016). We study random permutations of a given length from these classes, and in particular the number of occurrences of a fixed pattern in one of…
We study scaling limits of random permutations ("permutons") constrained by having fixed densities of a finite number of patterns. We show that the limit shapes are determined by maximizing entropy over permutons with those constraints. In…
The number of fixed points of a random permutation of 1,2,...,n has a limiting Poisson distribution. We seek a generalization, looking at other actions of the symmetric group. Restricting attention to primitive actions, a complete…
The spectrum of a local random Hamiltonian can be represented generically by the so-called $\epsilon$-free convolution of its local terms' probability distributions. We establish an isomorphism between the set of $\epsilon$-noncrossing…
We study proportions of consecutive occurrences of permutations of a given size. Specifically, the limit of such proportions on large permutations forms a region, called \emph{feasible region}. We show that this feasible region is a…
Permutations are usually enumerated by size, but new results can be found by enumerating them by inversions instead, in which case one must restrict one's attention to indecomposable permutations. In the style of the seminal paper by Simion…
In this work, we study the concept of self-overlapping permutations, which is related to the larger study of consecutive patterns in permutations. We show that this concept admits a simple and clear geometrical meaning, and prove that a…
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 processes in the plane. This enables the use of geometric tools…
Random permutations with distribution conditionally uniform given the set of record values can be generated in a unified way, coherently for all values of $n$. Our central example is a two-parameter family of random permutations that are…