Related papers: GUE Correlators and Large Genus Asymptotics

The eigenvalue correlations of random matrices from the Jacobi Unitary Ensemble have a known asymptotic behavior as their size tends to infinity. In the bulk of the spectrum the behavior is described in terms of the sine kernel, and at the…

We study asymptotics of reducible representations of the symmetric groups S_q for large q. We decompose such a representation as a sum of irreducible components (or, alternatively, Young diagrams) and we ask what is the character of a…

We study the quantitative behaviour of genus numbers of abelian extensions of number fields with given Galois group. We prove an asymptotic formula for the average value of the genus number and show that any given genus number appears only…

Let W be an affine PI algebra over a field of characteristic zero graded by a finite group G. We show that there exist $\alpha_{1},\alpha_{2}\in\mathbb{R}, \beta\in\frac{1}{2}\mathbb{Z}$, and $l\in\mathbb{N}$ such that…

We develop a theory of average sizes of kernels of generic matrices with support constraints defined in terms of graphs and hypergraphs. We apply this theory to study unipotent groups associated with graphs. In particular, we establish…

We investigate $\beta$-Generalized random Hermitian matrices ensemble sometimes called Chiral ensemble. We give global asymptotic of the density of eigenvalues or the statistical density. We investigate general method names as equilibrium…

We compute the spectral correlation functions for the transition from a harmonic oscillator towards the Gaussian Unitary Ensemble (GUE). We use a variant of the supersymmetry method to obtain analytical results in a fast and elegant way. In…

We prove that the asymptotic entropy of large simple graphs, as a function of fixed edge and triangle densities, is nondifferentiable along a certain curve.

The aim of this note is to prove that fluctuations of uniformly random alternating sign matrices (equivalently, configurations of the six-vertex model with domain wall boundary conditions) near the boundary are described by the Gaussian…

In this paper, we establish the existence of large solutions of Hessian equations and obtain a new boundary asymptotic behavior of solutions.

We compute the tail asymptotics of the product of a beta random variable and a generalized gamma random variable which are independent and have general parameters. A special case of these asymptotics were proved and used in a recent work of…

We enumerate factorisations of the complete graph into spanning regular graphs in several cases, including when the degrees of all the factors except for one or two are small. The resulting asymptotic behaviour is seen to generalise the…

For each $N\geq 1$, let $G_N$ be a simple random graph on the set of vertices $[N]=\{1,2, ..., N\}$, which is invariant by relabeling of the vertices. The asymptotic behavior as $N$ goes to infinity of correlation functions: $$ \mathfrak…

We give explicit formulas for the asymptotic Betti numbers, over an arbitrary field, of the ordered configuration spaces of a graph. In characteristic zero, we further give explicit formulas for the asymptotic multiplicities in homology of…

The well-known asymptotic formula for the module of a condenser with one of the plates degenerating to a point is generalized to the case of a condenser of general type. The condensers under consideration consist of n plates, n > 2, and the…

We consider the asymptotics of the second-order correlation function of the characteristic polynomial of a random matrix. We show that the known result for a random matrix from the Gaussian Unitary Ensemble essentially continues to hold for…

Consider the ideal I corresponding to r points in P^2. We study the symbolic generic initial system of I, formed by taking the generic initial ideals of the symbolic powers of I, and its asymptotic behaviour. In particular, we describe the…

In this paper we relate a fundamental parameter of a random graph, its degree sequence, to a simple model of nearly independent binomial random variables. This confirms a conjecture made in 1997. As a result, many interesting functions of…

A new approach to the problem of finding the asymptotical behaviour of large orders of semiclassical expansion is suggested. Asymptotics of high orders not only for eigenvalues, but also for eigenfunctions, are constructed. Thus, one can…

We perform the asymptotic enumeration of two classes of rooted maps on orientable surfaces of genus g: m-hypermaps and m-constellations. For m=2, they correspond respectively to maps with even face degrees and bipartite maps. We obtain…