Related papers: On the pair correlation statistics for determinant…
We present a microscopic theory of fluctuation-mediated pairing mechanism in a two-dimensional extended Hubbard model. In contrast to conventional wisdom, odd-frequency spin-triplet pairing can be stabilized near the spin-density-wave…
We study the global fluctuations for a class of determinantal point processes coming from large systems of non-colliding processes and non-intersecting paths. Our main assumption is that the point processes are constructed by biorthogonal…
Phase transitions in disordered systems can be smeared if rare spatial regions develop true static order while the bulk system is in the disordered phase. Here, we study the effects of spatial disorder correlations on such smeared phase…
For a class of one-dimensional determinantal point processes including those induced by orthogonal projections with integrable kernels satisfying a growth condition, it is proved that their conditional measures, with respect to the…
We propose and analyze a specific asymptotic stochastic order for random processes based on the measure of departure discussed in the literature. As applications, we stochastically compare mixtures of order statistics and record values…
The optimal matching of point clouds in $\mathbb{R}^d$ is a combinatorial problem; applications in statistics motivate to consider random point clouds, like the Poisson point process. There is a crucial dependance on dimension $d$, with…
The relative dispersion of pairs of inertial particles in incompressible, homogeneous, and isotropic turbulence is studied by means of direct numerical simulations at two values of the Taylor-scale Reynolds number $Re_{\lambda} \sim 200$…
We numerically analyze the random matrix ensembles of real-symmetric matrices with column/row constraints for many system conditions e.g. disorder type, matrix-size and basis-connectivity. The results reveal a rich behavior hidden beneath…
In this paper we study the geometric discrepancy of explicit constructions of uniformly distributed points on the two-dimensional unit sphere. We show that the spherical cap discrepancy of random point sets, of spherical digital nets and of…
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
The initial conditions of cosmological simulations are commonly drawn from a Gaussian ensemble. The limited number of modes inside a simulation volume gives rise to statistical fluctuations known as \textit{sample variance}, limiting the…
We investigate the average characteristic polynomial $\mathbb E\big[\prod_{i=1}^N(z-x_i)\big] $ where the $x_i$'s are real random variables which form a determinantal point process associated to a bounded projection operator. For a subclass…
The ability to tailor the spectral response of photonic devices is paramount to the advancement of a broad range of applications. The vast design space offered by disordered optical media provide enhanced functionality for spectral…
Determinantal point processes (DPPs) are probability models over subsets of a ground set that favor diverse selections while suppressing redundancy. That is, they tend to assign higher likelihood to collections whose elements complement one…
We consider a collection of weighted Euclidian random balls in R^d distributed according a determinantal point process. We perform a zoom-out procedure by shrinking the radii while increasing the number of balls. We observe that the…
This work is concerned with the estimation of the intensity parameter of a stationary determinantal point process. We consider the standard estimator, corresponding to the number of observed points per unit volume and a recently introduced…
A random recursive cell splitting scheme of the $2$-dimensional unit sphere is considered, which is the spherical analogue of the STIT tessellation process from Euclidean stochastic geometry. First-order moments are computed for a large…
Determinantal points processes are a promising but relatively under-developed tool in machine learning and statistical modelling, being the canonical statistical example of distributions with repulsion. While their mathematical formulation…
Determinantal point processes (DPPs) are an important concept in random matrix theory and combinatorics. They have also recently attracted interest in the study of numerical methods for machine learning, as they offer an elegant "missing…
Score matching is an estimation procedure that has been developed for statistical models whose probability density function is known up to proportionality but whose normalizing constant is intractable, so that maximum likelihood is…