相关论文: On the Limiting Shape of Young Tableaux Associated…

Let $(X_n)_{n \ge 0}$ be an irreducible, aperiodic, homogeneous Markov chain, with state space an ordered finite alphabet of size $m$. Using combinatorial constructions and weak invariance principles, we obtain the limiting shape of the…

Given a random word of size $n$ whose letters are drawn independently from an ordered alphabet of size $m$, the fluctuations of the shape of the random RSK Young tableaux are investigated, when $n$ and $m$ converge together to infinity. If…

We investigate the large deviations of the shape of the random RSK Young diagrams associated with a random word of size $n$ whose letters are independently drawn from an alphabet of size $m=m(n)$. When the letters are drawn uniformly and…

In this work we are considering the behavior of the limit shape of Young diagrams associated to random permutations on the set $\{1,\dots,n\}$ under a particular class of multiplicative measures. Our method is based on generating functions…

We present equalities in law between the spectra of the minors of a GUE matrix and some maximal functionals of independent Brownian motions. In turn, these results allow to recover the limiting shape (properly centered and scaled) of the…

We study asymptotics of random shifted Young diagrams which correspond to a given sequence of reducible projective representations of the symmetric groups. We show limit results (Law of Large Numbers and Central Limit Theorem) for their…

We revisit, beyond the uniform case, some aspects of the convergence of the cumulative shape of the RSK Young diagrams associated with random words, obtaining rates of convergence in Kolmogorov's distance. Since the length of the top row of…

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…

We introduce a large class of random Young diagrams which can be regarded as a natural one-parameter deformation of some classical Young diagram ensembles; a deformation which is related to Jack polynomials and Jack characters. We show that…

The complicated interactions in presence of disorder lead to a correlated randomization of states. The Hamiltonian as a result behaves like a multi-parametric random matrix with correlated elements. We show that the eigenvalue correlations…

The expectation of the descent number of a random Young tableau of a fixed shape is given, and concentration around the mean is shown. This result is generalized to the major index and to other descent functions. The proof combines…

The aim of this note is to describe the Poisson boundary of the group of invertible triangular matrices with coefficients in a number field. It generalizes to any dimension and to any number field a result of Brofferio concerning the…

Consider $q_n$ a random pointed quadrangulation chosen equally likely among the pointed quadrangulations with $n$ faces. In this paper we show that, when $n$ goes to $+\infty$, $q_n$ suitably normalized converges weakly in a certain sense…

We study the limiting shape of the connected components of the vacant set of two-dimensional Brownian random interlacements: we prove that the connected component around $x$ is close in distribution to a rescaled \emph{Brownian amoeba} in…

We consider large uniform labeled random graphs in different classes with prescribed decorations in their modular decomposition. Our main result is the estimation of the number of copies of every graph as an induced subgraph. As a…

We exhibit the limit shape of random Young diagrams having a distribution proportional to the exponential of their area, and confined in a rectangular box. The Ornstein-Uhlenbeck bridge arises from the fluctuations around the limit shape.

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…

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 consider the singular values of certain Young diagram shaped random matrices. For block-shaped random matrices, the empirical distribution of the squares of the singular eigenvalues converges almost surely to a distribution whose moments…

A non-Hermitean random matrix model proposed a few years ago has a remarkably intricate spectrum. Various attempts have been made to understand the spectrum, but even its dimension is not known. Using the Dyson-Schmidt equation, we show…