Related papers: Determinantal point processes on spheres: multivar…
We consider the determinantal point process with the confluent hypergeometric kernel. This process is a universal point process in random matrix theory and describes the distribution of eigenvalues of large random Hermitian matrices near…
We construct a canonical embedding of the space $L^2$ over a determinantal point process to the fermionic Fock space. Equivalently, we show that a determinantal process is the spectral measure for some explicit commutative group of Gaussian…
Comparisons of higher-order predictions within the Standard Model of Particle Physics (SM) to data are central to high-energy collider experiments like the Large Hadron Collider (LHC). Processes with multiple kinematic scales, such as…
We introduce a projective Riesz $s$-kernel for the unit sphere $\mathbb{S}^{d-1}$ and investigate properties of $N$-point energy minimizing configurations for such a kernel. We show that these configurations, for $s$ and $N$ sufficiently…
Recently, various convolutions based on continuous or discrete kernels for point cloud processing have been widely studied, and achieve impressive performance in many applications, such as shape classification, scene segmentation and so on.…
Differential measurements of particle collisions or decays can provide stringent constraints on physics beyond the Standard Model of particle physics. In particular, the distributions of the kinematical and angular variables that…
We consider heat kernels on Weyl chambers corresponding to Laplacians subject to mixed Dirichlet-Neumann boundary conditions imposed on the boundary. Using purely analytic tools we prove genuinely sharp two-sided global estimates in the…
We prove that the formula which gives the Wiener chaos decomposition of the multiplication of two multiple Wiener integrals with symmetric kernels is a straightforward application of the Leibniz' formula.
We investigate solutions of the 2d incompressible Euler equations, linearized around steady states which are radially decreasing vortices. Our main goal is to understand the smoothness of what we call the spectral density function…
This paper concerns space-sphere point processes, that is, point processes on the product space of $\mathbb R^d$ (the $d$-dimensional Euclidean space) and $\mathbb S^k$ (the $k$-dimen\-sional sphere). We consider specific classes of models…
Some Wiener--Hopf determinants on [0,s] are calculated explicitly for all s>0. Their symbols are zero on an interval and they are related to the determinant with the sine-kernel appearing in the random matrix theory. The determinants are…
We study parametric estimation for second order linear parabolic stochastic partial differential equations (SPDEs) in two space dimensions driven by two types of $Q$-Wiener processes based on high frequency spatio-temporal data. First, we…
Diffusion models have become a leading framework in generative modeling, yet their theoretical understanding -- especially for high-dimensional data concentrated on low-dimensional structures -- remains incomplete. This paper investigates…
We consider the behavior of spatial point processes when subjected to a class of linear transformations indexed by a variable T. It was shown in Ellis [Adv. in Appl. Probab. 18 (1986) 646-659] that, under mild assumptions, the transformed…
We compare Wiener chaos and stochastic collocation methods for linear advection-reaction-diffusion equations with multiplicative white noise. Both methods are constructed based on a recursive multi-stage algorithm for long-time integration.…
This paper contains a study of multivariate second order stochastic mappings indexed by an abstract set $\Lambda$ in close connection to their operator covariance functions. The characterizations of the normal Hilbert module or of Hilbert…
The physical parameters governing the dynamics of a light emitting quantum system can be estimated from the photon counting signal. The information available in the full detection record can be analysed by means of the distribution of…
Astrophysical images issued from different instruments and/or spectral bands often require to be processed together, either for fitting or comparison purposes. However each image is affected by an instrumental response, also known as PSF,…
In this note we present new examples of determinantal point processes with infinitely many particles. The particles live on the half-lattice {1,2,...} or on the open half-line (0,+\infty). The main result is the computation of the…
The use of multitaper estimates for spectral proper orthogonal decomposition (SPOD) is explored. Multitaper and multitaper-Welch estimators that use discrete prolate spheroidal sequences (DPSS) as orthogonal data windows are compared to the…