相关论文: Determinantal transition kernels for some interact…

We propose a data-driven framework to learn interaction kernels in stochastic multi-agent systems. Our approach aims at identifying the functional form of nonlocal interaction and diffusion terms directly from trajectory data, without any a…

We develop a Gaussian process framework for learning interaction kernels in multi-species interacting particle systems from trajectory data. Such systems provide a canonical setting for multiscale modeling, where simple microscopic…

This paper investigates the composition of Bernstein--Durrmeyer operators and Sz\'asz--Mirakjan--Durrmeyer operators, focusing on the structure and properties of the associated kernel functions. In the case of the Bernstein--Durrmeyer…

The multirank separable kernels of the neutron-proton interaction for uncoupled $S$ and $P$ partial waves (with the total angular momentum $J$=0,1) are proposed. Two different methods of a relativistic generalization of initially…

We study a general class of interacting particle systems over a countable state space $V$ where on each site $x \in V$ the particle mass $\eta(x) \geq 0$ follows a stochastic differential equation. We construct the corresponding Markovian…

All one-condition generalized inverses of the Markovian kernel I - P, where P is the transition matrix of a finite irreducible Markov chain, can be uniquely specified in terms of the stationary probabilities and the mean first passage times…

We obtain the memory kernel of the generalized Langevin equation, describing a particle interacting with longitudinal phonons in a liquid. The kernel is obtained analytically at T=0 Kelvin and numerically at T>0 Kelvin. We find that it…

We provide pointwise upper bounds for the transition kernels of semigroups associated with a class of systems of nondegenerate elliptic partial differential equations with unbounded coefficients with possibly unbounded diffusion…

We derive a cross-Kerr type effective Hamiltonian for the four-level atom interacting with three electromagnetic fields in the N-configuration. When the atom has relaxed into the ground state a cross-Kerr nonlinearity arises between two…

The paper studies an improved estimate for the rate of convergence for nonlinear homogeneous discrete-time Markov chains. These processes are nonlinear in terms of the distribution law. Hence, the transition kernels are dependent on the…

For a broad class of point processes, including determinantal point processes, we construct associated marked and conditional ensembles, which allow to study a random configuration in the point process, based on information about a randomly…

Integral kernels describing the pair interaction of reggeized gluons and quarks are reconstructed in terms of conformal symmetric 4-point functions in the transverse plane of impact parameters.

The paper contains an exposition of recent as well as old enough results on determinantal random point fields. We start with some general theorems including the proofs of the necessary and sufficient condition for the existence of the…

We consider the squared singular values of the product of $M$ standard complex Gaussian matrices. Since the squared singular values form a determinantal point process with a particular Meijer G-function kernel, the gap probabilities are…

We show that quantum optical systems preserving the total number of excitations admit a simple classification of possible resonant transitions (including effective), which can be classified by analizying the free Hamiltonian and the…

We study the kernel/metric correspondence pointed out in our previous work in a dissipative system which is accompanying fractional Brownian motion. We also give some comments on information causality.

We introduce a space inhomogeneous generalization of the dynamics on interlacing arrays considered by Borodin and Ferrari. We show that for a certain class of initial conditions the point process associated to the dynamics has determinantal…

We consider a one-dimensional system of Brownian particles that repel each other through a logarithmic potential. We study two formulations for the system and the relation between them. The first, Dyson's Brownian motion model, has an…

The dispersion relations for nucleon-nucleon (NN) T-matrix in the framework of Bethe-Salpeter equation for two spin one-half particle system and with separable kernel of interaction are considered in the paper. The developed expressions are…

The little q-Jacobi function transform depends on three parameters. An explicit expression as a sum of two very-well-poised 8W7-series is derived for the dual transmutation kernel (a kind of non-symmetric Poisson kernel) relating little…