Related papers: On statistics of permutations chosen from the Ewen…
The purpose of this article is to present a general method to find limiting laws for some renormalized statistics on random permutations. The model considered here is Ewens sampling model, which generalizes uniform random permutations. We…
We consider a generalization of the Ewens measure for the symmetric group, calculating moments of the characteristic polynomial and similar multiplicative statistics. In addition, we study the asymptotic behavior of linear statistics (such…
We study the limiting behavior of smooth linear statistics of the spectrum of random permutation matrices in the mesoscopic regime, when the permutation follows one of the Ewens measures on the symmetric group. If we apply a smooth enough…
The goal of this paper is to analyse the asymptotic behavior of the cycle process and the total number of cycles of weighted and generalized weighted random permutations which are relevant models in physics and which extend the Ewens…
We establish asymptotic expansions for factorial moments of following distributions: number of cycles in a random permutation, number of inversions in a random permutation, and number of comparisons used by the randomized quick sort…
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…
We propose an extension of the Ewens measure on permutations by choosing the cycle weights to be asymptotically proportional to the degree of the symmetric group. This model is primarily motivated by a natural approximation to the so-called…
We consider Ewens random permutations of length $n$ conditioned to have no cycle longer than $n^\beta$ with $0<\beta<1$ and to study the asymptotic behaviour as $n\to\infty$. We obtain very precise information on the joint distribution of…
The variance of a linear statistic defined on the symmetric group endowed with the Ewens probability is examined. Despite the dependence of the summands, it can be bounded from above by a constant multiple of the sum of variances. We find…
This paper develops an analogy between the cycle structure of, on the one hand, random permutations with cycle lengths restricted to lie in an infinite set $S$ with asymptotic density $\sigma$ and, on the other hand, permutations selected…
We study the number of random permutations needed to invariably generate the symmetric group, $S_n$, when the distribution of cycle counts has the strong $\alpha$-logarithmic property. The canonical example is the Ewens sampling formula,…
We consider the logarithm of the characteristic polynomial of random permutation matrices, evaluated on a finite set of different points. The permutations are chosen with respect to the Ewens distribution on the symmetric group. We show…
An involution is a bijection that is its own inverse. Given a permutation $\sigma$ of $[n],$ let $\mathsf{invol}(\sigma)$ denote the number of ways $\sigma$ can be expressed as a composition of two involutions of $[n].$ We prove that the…
From the distributional characterizations that lie at the heart of Stein's method we derive explicit formulae for the mass functions of discrete probability laws that identify those distributions. These identities are applied to develop…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is discussed. A wide set of measurable quantities ("invariant moments") whose expectation value…
We present a class of positive discrete random variables extending the Conway--Maxwell-Poisson distribution. This class emerges in a natural way from an application in queueing theory and contains distributions exhibiting quite different…
Smooth linear statistics of random permutation matrices, sampled under a general Ewens distribution, exhibit an interesting non-universality phenomenon. Though they have bounded variance, their fluctuations are asymptotically non-Gaussian…
The second author had previously obtained explicit generating functions for moments of characteristic polynomials of permutation matrices (n points). In this paper, we generalize many aspects of this situation. We introduce random shifts of…
We show that the number of cycles in a random permutation chosen according to generalized Ewens measure is normally distributed and compute asymptotic estimates for the mean and variance.
We prove several general formulas for the distributions of various permutation statistics over any set of permutations whose quasisymmetric generating function is a symmetric function. Our formulas involve certain kinds of plethystic…