Related papers: Long-time asymptotics for multivariate Hawkes proc…
An effect generated by the nonexponential behavior of the survival amplitude of an unstable state at the long time region is considered. It is known that this amplitude tends to zero as $t$ goes to the infinity more slowly than any…
Interacting Fock space connects the study of quantum probability theory, classical random variables, and orthogonal polynomials. It is a pre-Hilbert space associated with creation, preservation, and annihilation processes. We prove that if…
This paper analyzes the limit properties of the empirical process of $\alpha$-stable random variables with long range dependence. The $\alpha$-stable random variables are constructed by non-linear transformations of bivariate sequences of…
In non-relativistic quantum theories with short-range Hamiltonians, a velocity $v$ can be chosen such that the influence of any local perturbation is approximately confined to within a distance $r$ until a time $t \sim r/v$, thereby…
We introduce a numerical algorithm to simulate the time evolution of a matrix product state under a long-ranged Hamiltonian. In the effectively one-dimensional representation of a system by matrix product states, long-ranged interactions…
We extend the theory of quantum quenches to the case of $d$-dimensional homogeneous systems with long range interactions. This is achieved treating the long range interactions as switched on by the quench and performing the derivation…
Recent theoretical studies of statistical mechanical properties of systems with long range interactions are briefly reviewed. In these systems the interaction potential decays with a rate slower than 1/r^d at large distances r in d…
The relaxation of uniform quantum systems with finite-range interactions after a quench is generically driven by the ballistic propagation of long-lived quasi-particle excitations triggered by a sufficiently small quench. Here we…
We study 1D Hamilton systems with homogeneous power law potential and their statistical behaviour, assuming the microcanonical distribution of the initial conditions and describing its change under monotonically increasing time-dependent…
In this paper, we build a model for biological neural nets where the activity of the network is described by Hawkes processes having a variable length memory. The particularity of this paper is to deal with an infinite number of components.…
In this paper, we study a class of self-exciting point processes. The intensity of the point process has a nonlinear dependence on the past history and time. When a new jump occurs, the intensity increases and we expect more jumps to come.…
The dynamics of interacting dark matter-dark energy models is characterized through an interaction rate function quantifying the energy flow between these dark sectors. In most of the interaction functions, the expansion rate Hubble…
Inferring the laws of interaction between particles and agents in complex dynamical systems from observational data is a fundamental challenge in a wide variety of disciplines. We propose a non-parametric statistical learning approach to…
We numerically study a one-dimensional system of $N$ classical localized planar rotators coupled through interactions which decay with distance as $1/r^\alpha$ ($\alpha \ge 0$). The approach is a first principle one (\textit{i.e.}, based on…
We extract the long-distance asymptotic behaviour of two-point correlation functions in massless quantum integrable models containing multi-species excitations. For such a purpose, we extend to these models the method of a large-distance…
In this paper we study long-term evolution of a finite system of locally interacting birth-and-death processes labelled by vertices of a finite connected graph. A detailed description of the asymptotic behaviour is obtained in the case of…
Properties of strong mixing have been established for the stationary linear Hawkes process in the univariate case, and can serve as a basis for statistical applications. In this paper, we provide the technical arguments needed to extend the…
In this study, we reexamine the long-range interaction between two atoms placed in an equilibrium thermal radiation environment. Employing the formalism of quantum electrodynamics at finite temperatures, we derive an expression for the…
There are problems with defining the thermodynamic limit of systems with long-range interactions; as a result, the thermodynamic behavior of these types of systems is anomalous. In the present work, we review some concepts from both…
We investigate the behavior of the asymptotic late-times effective equation of state for a class of nonlocal theories of gravity. These theories modify the Einstein-Hilbert Lagrangian introducing terms containing negative powers of the…