相关论文: Asymptotic statistics of cycles in surrogate-spati…

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 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 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 explore the asymptotic distributions of sequences of integer-valued additive functions defined on the symmetric group endowed with the Ewens probability measure as the order of the group increases. Applying the method of factorial…

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 spatial permutations with cycle weights that are bounded or slowly diverging. We show that a phase transition occurs at an explicit critical density. The long cycles are macroscopic and their cycle lengths satisfy a…

This is my dissertation. Its research object is a symmetric group of permutations acting on a finite set. The density of permutations with a given cycle structure pattern is explored when the group order tends to infinity. New and sharper…

We study the asymptotic behavior of short cycles of random permutations with cycle weights. More specifically, on a specially constructed metric space whose elements encode all possible cycles, we consider a point process containing all…

We prove some general results about the asymptotics of the distribution of the number of cycles of given length of a random permutation whose distribution is invariant under conjugation. These results were first established to be applied in…

We study the length of cycles in the model of spatial random permutations in Euclidean space. In this model, for given length $L$, density $\rho$, dimension $d$ and jump density $\varphi$, one samples $\rho L^d$ particles in a…

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 investigate a model of random spatial permutations on two-dimensional tori, and establish that the joint distribution of large cycles is asymptotically given by the Poisson--Dirichlet distribution with parameter one. The asymmetry of the…

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.

For uniform random permutations conditioned to have no long cycles, we prove that the total number of cycles satisfies a central limit theorem. Under additional assumptions on the asymptotic behavior of the set of allowed cycle lengths, we…

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 study the asymptotic behavior of the long cycles of a random permutation of $n$ objects with respect to multiplicative measures with polynomial growing cycle weights. We show that the longest cycle and the length differences between the…

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 consider random permutations on $\Sn$ with logarithmic growing cycles weights and study asymptotic behavior as the length $n$ tends to infinity. We show that the cycle count process converges to a vector of independent Poisson variables…

We consider the distribution of cycles in two models of random permutations, that are related to one another. In the first model, cycles receive a weight that depends on their length. The second model deals with permutations of points in…