Related papers: Random Permutations -- A geometric point of view

We study a limit behavior of a sequence of Markov processes (or Markov chains) such that their distributions outside of any neighborhood of a "singular" point attract to some probability law. In any neighborhood of this point the behavior…

This work will appear as a chapter in a forthcoming volume titled "Topics in Probabilistic Graph Theory". A theory of scaling limits for random graphs has been developed in recent years. This theory gives access to the large-scale geometric…

We consider random permutation matrices following a one-parameter family of deformations of the uniform distribution, called Ewens' measures, and modifications of these matrices where the entries equal to one are replaced by i.i.d uniform…

We introduce a new natural notion of convergence for permutations at any specified scale, in terms of the density of patterns of restricted width. In this setting we prove that limits may be chosen independently at a countably infinite…

In this article, we consider limit theorems for some weighted type random sums (or discrete rough integrals). We introduce a general transfer principle from limit theorems for unweighted sums to limit theorems for weighted sums via rough…

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 consider random rooted maps without regard to their genus, with fixed large number of edges, and address the problem of limiting distributions for six different parameters: vertices, leaves, loops, root edges, root isthmus, and root…

The theory of limits of permutations leads to limit objects called permutons, which are certain Borel measures on the unit square. We prove that permutons avoiding a given permutation of order $k$ have a particularly simple structure.…

In the course of classifying the homogeneous permutations, Cameron introduced the viewpoint of permutations as structures in a language of two linear orders, and this structural viewpoint is taken up here. The majority of this thesis is…

Consider a family of random ordered graph trees $(T_n)_{n\geq 1}$, where $T_n$ has $n$ vertices. It has previously been established that if the associated search-depth processes converge to the normalised Brownian excursion when rescaled…

Restrictions to molecular motion by barriers (membranes) are ubiquitous in biological tissues, porous media and composite materials. A major challenge is to characterize the microstructure of a material or an organism nondestructively using…

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…

One object of interest in random matrix theory is a family of point ensembles (random point configurations) related to various systems of classical orthogonal polynomials. The paper deals with a one--parametric deformation of these…

Let $G_{k,n}$ be a group of permutations of $kn$ objects which permutes things independently in disjoint blocks of size $k$ and then permutes the blocks. We investigate the probabilistic and/or enumerative aspects of random elements of…

A locally uniform random permutation is generated by sampling $n$ points independently from some absolutely continuous distribution $\rho$ on the plane and interpreting them as a permutation by the rule that $i$ maps to $j$ if the $i$th…

A permutation of size $n$ can be identified to its diagram in which there is exactly one point per row and column in the grid $[n]^2$. In this paper we consider multidimensional permutations (or $d$-permutations), which are identified to…

We construct and analyze several new families of permutons arising from random processes involving the Demazure product on the symmetric group. First, we consider Demazure products associated to random pipe dreams, generalizing the…

We present different continuous models of random geometry that have been introduced and studied in the recent years. In particular, we consider the Brownian map, which is the universal scaling limit of large planar maps in the…

We introduce a permutation analogue of the celebrated Szemeredi Regularity Lemma, and derive a number of consequences. This tool allows us to provide a structural description of permutations which avoid a specified pattern, a result that…

We study the distribution of cycle lengths in models of nonuniform random permutations with cycle weights. We identify several regimes. Depending on the weights, the length of typical cycles grows like the total number $n$ of elements, or a…