Related papers: Difference operators and determinantal point proce…
Determinantal process is a dynamical extension of a determinantal point process such that any spatio-temporal correlation function is given by a determinant specified by a single continuous function called the correlation kernel.…
This paper investigates the information geometrical structure of a determinantal point process (DPP). It demonstrates that a DPP is embedded in the exponential family of log-linear models. The extent of deviation from an exponential family…
Transfer operators such as the Perron--Frobenius or Koopman operator play an important role in the global analysis of complex dynamical systems. The eigenfunctions of these operators can be used to detect metastable sets, to project the…
Complete sets of bases of differential invariants, operators of invariant differentiation and Lie determinants of continuous transformation groups acting on the real plane are constructed. As a necessary preliminary, realizations of…
We study Sturm-Liouville operators on closed sets of a special structure, which are sometimes referred as time scales and often appear in modelling various real processes. Depending on the set structure, such operators unify both…
We consider the analytic continuation of the transfer function for a 2x2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct a family of non-selfadjoint operators which reproduce certain parts of the…
This paper explores operators with countable, continuous, and hybrid spectra, focusing on both finite dimensional and infinite dimensional cases, particularly in non-Hermitian systems. For finite dimensional operators, a novel concept of…
In this paper, we will investigate the jet schemes of determinantal varieties. It is quite often the case that the geometric information concerning the jet schemes of an algebraic variety can be described, but the more refined algebraic…
A lattice diagram is a finite list L=((p_1,q_1),...,(p_n,q_n) of lattice cells. The corresponding lattice diagram determinant is \Delta_L(X;Y)=\det \| x_i^{p_j}y_i^{q_j} \|. These lattice diagram determinants are crucial in the study of the…
The aim of this paper is to present a study on the representations of coordinate, momentum and dispersion operators in the framework of a phase space representation of quantum mechanics that we have introduced and studied in previous works.…
Motivated by practical applications, I present a novel and comprehensive framework for operator-valued positive definite kernels. This framework is applied to both operator theory and stochastic processes. The first application focuses on…
Determinantal point processes (DPPs) are random point processes well-suited for modeling repulsion. In machine learning, the focus of DPP-based models has been on diverse subset selection from a discrete and finite base set. This discrete…
Many interesting families of polynomials are indexed by permutations or related objects, and are defined by applying divided difference operators, modified by polynomials, on some initial base case. The fact that these constructions produce…
Matrix Dirichlet processes, in reference to their reversible measure, appear in a natural way in many different models in probability. Applying the language of diffusion operators and the method of boundary equations, we describe Dirichlet…
The Ginibre point process is one of the main examples of deter- minantal point processes on the complex plane. It forms a recurring model in stochastic matrix theory as well as in pratical applications. However, this model has mostly been…
We consider determinantal point processes on the $d$-dimensional unit sphere $\mathbb S^d$. These are finite point processes exhibiting repulsiveness and with moment properties determined by a certain determinant whose entries are specified…
Quantum Iterated Function System on a complex projective space is defined by a family of linear operators on a complex Hilbert space. The operators define both the maps and their probabilities by one algebraic formula. Examples with…
In the article we study properties of the random integral operator in $L_2(\mathbb{R})$ whose kernel is obtained as a convolution of Gaussian density with a stationary point process.
Martingale techniques play a fundamental role in the analysis of point processes on the real line. In particular, the compensator of a point process uniquely determines and is determined by its distribution, and an explicit formula…
Representations of polynomial covariance commutation relations by pairs of linear integral and differential operators are constructed in the space of infinitely continuously differentiable functions. Representations of polynomial covariance…