Related papers: The limit shape of random permutations with polyno…

In a series of works published in the 1990-s, Kerov put forth various applications of the circle of ideas centred at the Markov moment problem to the limiting shape of random continual diagrams arising in representation theory and spectral…

Using the recently developed notion of permutation limits this paper derives the limiting distribution of the number of fixed points and cycle structure for any convergent sequence of random permutations, under mild regularity conditions.…

We give a method for taking microscopic limits of normal matrix ensembles. We apply this method to study the behaviour near certain types of singular points on the boundary of the droplet. Our investigation includes ensembles without…

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…

We investigate the asymptotic properties of permutations drawn from the Luce model, a natural probabilistic framework in which permutations are generated sequentially by sampling without replacement, with selection probabilities…

It has been shown by Pittel and Romik that the random surface associated with a large rectangular Young tableau converges to a deterministic limit. We study the fluctuations from this limit along the edges of the rectangle. We show that in…

The work of Vershik and Kerov [1977], Logan and Shepp [1977] established that the shape of the scaled random young diagram in Russian notation, as determined by the Plancherel measure, converges to a deterministic shape. In this article, we…

We consider the probability measures on Young diagrams in the $n \times k$ rectangle obtained by piecewise-continuously differentiable specializations of Schur polynomials in the dual Cauchy identity. We use a free fermionic representation…

We consider uniform random permutations in classes having a finite combinatorial specification for the substitution decomposition. These classes include (but are not limited to) all permutation classes with a finite number of simple…

The limiting shape of the random Young diagrams associated with an inhomogeneous random word is identified as a multidimensional Brownian functional. This functional is identical in law to the spectrum of a random matrix. The Poissonized…

In random tiling and dimer models we can get various limit shapes which gives the boundaries between different types of phases. The shape fluctuations at these boundaries give rise to universal limit laws, in particular the Airy process. We…

We derive the limit shape of Young diagrams, associated with growing integer partitions, with respect to multiplicative probability measures underpinned by the generating functions of the form $\mathcal{F}(z)=\prod_{\ell=1}^\infty…

We obtain scaling and local limit results for large random Young tableaux of fixed shape $\lambda^0$ via the asymptotic analysis of a determinantal point process due to Gorin and Rahman (2019). More precisely, we prove: (1) an explicit…

In this paper, we study the fluctuations of sums of random variables with distribution defined as a mixture of light-tail and truncated heavy-tail distributions. We focus on the case when both the mixing coefficient and the truncation level…

We present a survey of points of view on the problem of the asymptotic shape of a path between two large Young diagrams, and introduce a modification of the TASEP process related to it. This representation allows to write explicitly the…

This paper studies thresholds in random generalized Johnson graphs for containing large cycles, i.e. cycles of variable length growing with the size of the graph. Thresholds are obtained for different growth rates.

For a subfamily of multiplicative measures on integer partitions we give conditions for properly rescaled associated Young diagrams to converge in probability to a certain deterministic curve named the limit shape of partitions. We provide…

We consider the multi-point equal time height fluctuations of a one-dimensional polynuclear growth model in a half space. For special values of the nucleation rate at the origin, the multi-layer version of the model is reduced to a…

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…

A single permutation, seen as union of disjoint cycles, represents a regular graph of degree two. Consider $d$ many independent random permutations and superimpose their graph structures. It is a common model of a random regular (multi-)…