Related papers: Asymptotics of random Betti tables
A discrete Gelfand-Tsetlin pattern is a configuration of particles in Z^2. The particles are arranged in a finite number of consecutive rows, numbered from the bottom. There is one particle on the first row, two particles on the second row,…
Amit and Linial showed that a random lift of a graph with minimum degree $\delta\ge3$ is asymptotically almost surely $\delta$-connected, and mentioned the problem of estimating this probability as a function of the degree of the lift. We…
Specimens are collected from $N$ different sources. Each specimen has probability $p$ of being contaminated, independently of the other specimens. We assume group testing is applicable, namely one can take small portions from several…
Given an elliptic self-adjoint pseudo-differential operator $P$ bounded from below, acting on the sections of a Riemannian line bundle over a smooth closed manifold $M$ equipped with some Lebesgue measure, we estimate from above, as $L$…
In this paper, we study staircase tableaux, a combinatorial object introduced due to its connections with the asymmetric exclusion process (ASEP) and Askey-Wilson polynomials. Due to their interesting connections, staircase tableaux have…
This paper is mainly concerned with asymptotic studies of weighted bootstrap for u- and v-statistics. We derive the consistency of the weighted bootstrap u- and v-statistics, based on i.i.d. and non i.i.d. observations, from some more…
This paper studies the asymptotic behavior of the flux and circulation of a subclass of random fields within the family of 2-dimensional vector ambit fields. We show that, under proper normalization, the flux and the circulation converge…
We compute analytically the joint probability density of eigenvalues and the level spacing statistics for an ensemble of random matrices with interesting features. It is invariant under the standard symmetry groups (orthogonal and unitary)…
We study the asymptotic rank of adjacency matrices of a large class of edge-weighted configuration models. Here, the weight of a (multi-)edge can be any fixed non-zero element from an arbitrary field, as long as it is independent of the…
We describe the asymptotic properties of the edge-triangle exponential random graph model as the natural parameters diverge along straight lines. We show that as we continuously vary the slopes of these lines, a typical graph drawn from…
We study the distribution of the order of a random permutation of $[n]$ through the lens of R\'enyi entropy. In particular, we obtain an asymptotic for the R\'enyi $q$-entropy of the order in the full range $1 \leq q \leq \infty$. For $q >…
We study the asymptotic properties of the conormal cycle of nodal sets associated to a random superposition of eigenfunctions of the Laplacian on a smooth compact Riemannian manifold without boundary. In the case where the dimension is odd,…
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 give an asymptotic formula for the number of $\mathbb{F}_{q}$-rational points over a fixed determinant moduli space of stable vector bundles of rank $r$ and degree $d$ over a smooth, projective curve $X$ of genus $g \geq 2$ defined over…
The aim of the paper is to address the behavior in large population of diffusions interacting on a random, possibly diluted and inhomogeneous graph. This is the natural continuation of a previous work, where the homogeneous Erd\H os-R\'enyi…
We give explicit formulas for the asymptotic Betti numbers of the unordered configuration spaces of an arbitrary finite graph over an arbitrary field.
The purpose of this paper is to define and study systematically some asymptotic invariants associated to base loci of line bundles on smooth projective varieties. We distinguish an open dense subset of the real big cone, called the stable…
We study some new isoperimetric inequalities on graphs. We etablish a relation between the volume entropy (or asymptotic volume), the systole and the first Betti number of weighted graphs. We also find bounds for the volume, associated to…
We consider random graphs sampled uniformly from a structured class of graphs, such as the class of graphs embeddable in a given surface. We sharpen and extend earlier results on pendant appearances, concerning for example numbers of…
In this article, we investigate the stability of syzygy bundles corresponding to ample and globally generated vector bundles on smooth irreducible projective surfaces.