Related papers: Universality properties of Gelfand-Tsetlin pattern…
We show that the Riemannian Gaussian distributions on symmetric spaces, introduced in recent years, are of standard random matrix type. We exploit this to compute analytically marginals of the probability density functions. This can be done…
We establish a definition of ordinal patterns for multivariate data sets based on the concept of Tukey's halfspace depth. Given the definition of these \emph{depth patterns}, we are interested in the probabilities of observing specific…
We consider consistent particle systems, which include independent random walkers, the symmetric exclusion and inclusion processes, as well as the dual of the KMP model. Consistent systems are such that the distribution obtained by first…
Let f_n denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let \Psi(t) be a positive continuous function such that \|\Psi f^{\beta}\|_{\infty}<\infty for some 0<\beta<1/2. Under natural…
We study the convergence of Bernstein type operators leading to two results. The first: The kernel $K_n$ of the Bernstein-Durrmeyer operator at each point $x \in (0, 1)$ $\unicode{x2013}$ that is $K_n(x, t) dt$ $\unicode{x2013}$ once…
We present a solution to a problem suggested by Philippe Biane: We prove that a certain Plancherel-type probability distribution on partitions converges, as partitions get large, to a new determinantal random point process on the set…
A random geometric digraph $G_n$ is constructed by taking $\{X_1,X_2,... X_n\}$ in $\mathbb{R}^2$ independently at random with a common bounded density function. Each vertex $X_i$ is assigned at random a sector $S_i$ of central angle…
Motivated by the problem of compressing point sets into as few bits as possible while maintaining information about approximate distances between points, we construct random nonlinear maps $\varphi_\ell$ that compress point sets in the…
In this paper we study the concentration properties for the eigenvalues of kernel matrices, which are central objects in a wide range of kernel methods and, more recently, in network analysis. We present a set of concentration inequalities…
The eigenvalue probability density functions of the classical random matrix ensembles have a well known analogy with the one component log-gas at the special couplings \beta = 1,2 and 4. It has been known for some time that there is an…
We investigate a two-dimensional statistical model of N charged particles interacting via logarithmic repulsion in the presence of an oppositely charged compact region K whose charge density is determined by its equilibrium potential at an…
Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…
We consider a general class of $N\times N$ random matrices whose entries $h_{ij}$ are independent up to a symmetry constraint, but not necessarily identically distributed. Our main result is a local semicircle law which improves previous…
The concept of typical and weighted typical spherical faces for tessellations of the $d$-dimensional unit sphere, generated by $n$ independent random great hyperspheres distributed according to a non-degenerate directional distribution, is…
The scaled standard Wigner matrix (symmetric with mean zero, variance one i.i.d. entries), and its limiting eigenvalue distribution, namely the semi-circular distribution, has attracted much attention. The $2k$th moment of the limit equals…
This paper studies sparse elliptic random matrix models which generalize both the classical elliptic ensembles and sparse i.i.d. matrix models by incorporating correlated entries and a tunable sparsity parameter $p_n$. Each $n\times n$…
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…
The goal of this paper is to quantitatively describe some statistical properties of higher-dimensional determinantal point processes with a primary focus on the nearest-neighbor distribution functions. Toward this end, we express these…
Correlation matrices are the sub-class of positive definite real matrices with all entries on the diagonal equal to unity. Earlier work has exhibited a parametrisation of the corresponding Cholesky factorisation in terms of partial…
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)…