Related papers: Stationarity of multivariate particle systems
The formalism of the particle dynamics in the space-time, where motion of free particles is primordially stochastic, is considered. The conventional dynamic formalism, obtained for the space-time, where the motion of free particles is…
We present here a set of lecture notes on quantum systems with time-dependent boundaries. In particular, we analyze the dynamics of a non-relativistic particle in a bounded domain of physical space, when the boundaries are moving or…
We study the stochastic dynamics of a system of interacting species in a stochastic environment by means of a continuous-time Markov chain with transition rates depending on the state of the environment. Models of gene regulation in systems…
We study a generalization of the Brownian bridge as a stochastic process that models the position and velocity of inertial particles between the two end-points of a time interval. The particles experience random acceleration and are assumed…
In the paper is discussed complete probabilistic description of quantum systems with application to multiqubit quantum computations. In simplest case it is a set of probabilities of transitions to some fixed set of states. The probabilities…
We define a class of sequences ${a_n}$ by $a_1=a$ and $a_{n+1}=P(a_n)$, where $P(x)$ is a polynomial with real coefficients. We then find out for which values $a$ and for which polynomials $P(x)$ these sequences will be constant after a…
It is shown that a positive linear system on a time scale with a bounded graininess is uniformly exponentially stable if and only if the characteristic polynomial of the matrix defining the system has all its coefficients positive. Then…
We study stationary stable processes related to periodic and cyclic flows in the sense of Rosinski [Ann. Probab. 23 (1995) 1163-1187]. These processes are not ergodic. We provide their canonical representations, consider examples and show…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
We study a stochastic $N$-particle system representing economic agents in a population randomly exchanging their money, which is associated to a class of one-dimensional kinetic equations modelling the evolution of the distribution of…
We study measures on random partitions, arising from condensing stochastic particle systems with stationary product distributions. We provide fairly general conditions on the stationary weights, which lead to Poisson-Dirichlet statistics of…
We consider reaction-diffusion systems with multiplicative noise on a spatial domain of dimension two or higher. The noise process is white in time, coloured in space, and invariant under translations. In the deterministic setting,…
In this paper, the problem of partial stabilization of nonlinear systems along a given trajectory is considered. This problem is treated within the framework of stability of a family of sets. Sufficient conditions for the asymptotic…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
We construct a stochastic process whose drift is a function of the process's local time at a reflecting barrier. The process arose as a model of the interactions of a Brownian particle and an inert particle in (Knight, 2001). Interesting…
Studying systems where many individual bodies in motion interact with one another is a complex and interesting area. Simple mechanisms that may be determined for biological, chemical, or physical reasons can lead to astonishingly complex…
In this Letter we consider stationary states of dissipative quantum systems. We discuss stationary states of dissipative quantum systems, which coincide with stationary states of Hamiltonian quantum systems. Dissipative quantum systems with…
We consider the motion of a point particle with spin in a stationary spacetime. We define, following Witzany (2019) and later Ramond (2022), a twelve dimensional Hamiltonian dynamical system whose orbits coincide with the solutions of the…
The parameter region of multistationarity of a reaction network contains all the parameters for which the associated dynamical system exhibits multiple steady states. Describing this region is challenging and remains an active area of…
Motivated by a general principle governing regulation mechanisms in biological cells, we investigate a general interaction scheme between different populations of particles and specific particles, referred to as agents. Assuming that each…