Related papers: Markov evolutions and hierarchical equations in th…
The paper deals with the problem of the rigorous description of the evolution of states of large particle quantum systems by means of correlation operators. A nonperturbative solution of the Cauchy problem of the hierarchy of nonlinear…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
We consider a continuous time Markov process on $\mathbb{N}_0$ which can be interpreted as generalized alternating birth-death process in a non-autonomous random environment. Depending on the status of the environment the process either…
This paper is the second of two papers devoted to the study of the evolution of the cosmological horizons (particle and event horizons). Specifically, in this paper we consider the extremely general case of an accelerated universe with…
Infinite population models are important tools for studying population dynamics of evolutionary algorithms. They describe how the distributions of populations change between consecutive generations. In general, infinite population models…
Uncertainty, characterised by randomness and stochasticity, is ubiquitous in applications of evolutionary game theory across various fields, including biology, economics and social sciences. The uncertainty may arise from various sources…
We consider general convolutional derivatives and related fractional statistical dynamics of continuous interacting particle systems. We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum…
Systems out of equilibrium, in stationary as well as in nonstationary regimes, display a linear response to energy impulses simply expressed as the sum of two specific temporal correlation functions. There is a natural interpretation of…
Large ensembles of stochastically evolving interacting particles describe phenomena in diverse fields including statistical physics, neuroscience, biology, and engineering. In such systems, the infinitesimal evolution of each particle…
It is shown that a class of important integrable nonlinear evolution equations in (2+1) dimensions can be associated with the motion of space curves endowed with an extra spatial variable or equivalently, moving surfaces. Geometrical…
The contact process is a particular case of birth-and-death processes on infinite particle configurations. We consider the contact models on locally compact separable metric spaces. We prove the existence of a one-parameter set of invariant…
A mathematical model of the cosmological evolution of statistical systems of scalarly charged particles with Higgs scalar interaction is formulated and investigated. Examples are given of numerical modeling of such systems, revealing their…
We consider Markov chains on partially ordered sets that generalize the success-runs and remaining life chains in reliability theory. We find conditions for recurrence and transience and give simple expressions for the invariant…
We review some recent progresses in study of the 1D strongly correlated electron systems of long range hopping and exchange. The systems are completely integrable, with infinite number of constants of motions. The results of the physical…
A classical approach for the analysis of the longtime behavior of Markov processes is to consider suitable Lyapunov functionals like the variance or more generally $\Phi$-entropies. Via purely analytic arguments it can be shown that these…
We consider an open quantum many-particle system in which there are dissipative processes. The evolution of this system is described by a kinetic equation for the density matrix. From the equation describing a random Markov process in this…
We study a general class of translation invariant quantum Markov evolutions for a particle on $\bbZ^d$. The evolution consists of free flow, interrupted by scattering events. We assume spatial locality of the scattering events and…
Dynamics near and far away from thermal equilibrium is studied within the framework of Langevin equations. A stochasticity-dissipation relation is proposed to emphasize the equal importance of the stochastic and deterministic forces in…
Order-preserving couplings are elegant tools for obtaining robust estimates of the time-dependent and stationary distributions of Markov processes that are too complex to be analyzed exactly. The starting point of this paper is to study…
We construct a large class of completely positive and trace preserving non-Markovian dynamical maps for an open quantum system. These maps arise from a piecewise dynamics characterized by a continuous time evolution interrupted by jumps,…