Related papers: Open Markov chains: cumulant dynamics, fluctuation…
The dynamics of particles interacting by key-lock binding of attached biomolecules are studied theoretically. Examples of such systems include DNA-functionalized colloids as well as nanoparticles grafted with antibodies to cell membrane…
Normally, in mathematics and physics, only point particle systems, which are either finite or countable, are studied. We introduce new formal mathematical object called regular continuum system of point particles (with continuum number of…
In this work we study a branching particle system of diffusion processes on the real line interacting through their rank in the system. Namely, each particle follows an independent Brownian motion, but only K $\ge$ 1 particles on the far…
Population dynamics are often subject to random independent changes in the environment. For the two strategy stochastic replicator dynamic, we assume that stochastic changes in the environment replace the payoffs and variance. This is…
We consider a Markov chain of point processes such that each state is a super position of an independent cluster process with the previous state as its centre process together with some independent noise process. The model extends earlier…
Inspired by recent studies on deterministic oscillator models, we introduce a stochastic one-dimensional model for a chain of interacting particles. The model consists of $N$ oscillators performing continuous-time random walks on the…
We consider a system of $N$ identical independent Markov processes, each taking values 0 or 1. The system describes a stochastic dynamics of an ensemble of two-level atoms. The atoms are exposed to a photon flux. Under the photon flux…
We consider a multilevel continuous time Markov chain $X(s;N) = (X_i^j(s;N): 1 \leq i \leq j \leq N)$, which is defined by means of Jack symmetric functions and forms a certain discretization of the multilevel Dyson Brownian motion. The…
From the perspective of probability, the stability of growing network is studied in the present paper. Using the DMS model as an example, we establish a relation between the growing network and Markov process. Based on the concept and…
We study a system of particles moving on a line in the same direction. Passing is allowed and when a fast particle overtakes a slow particle, it acquires a new velocity drawn from a distribution P_0(v), while the slow particle remains…
We define the concept of an "open" Markov process, or more precisely, continuous-time Markov chain, which is one where probability can flow in or out of certain states called "inputs" and "outputs". One can build up a Markov process from…
A Multi-Agent System is a distributed system where the agents or nodes perform complex functions that cannot be written down in analytic form. Multi-Agent Systems are highly connected, and the information they contain is mostly stored in…
We examine reaction networks (CRNs) through their associated continuous-time Markov processes. Studying the dynamics of such networks is in general hard, both analytically and by simulation. In particular, stationary distributions of…
We study a driven system in which interaction between particles causes their directional, coupled movement. In that model system, two particles move alternatingly in time on two coupled chains. Without interaction, both particles diffuse…
We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of…
The information encoded into an open quantum system that evolves under a Markovian dynamics is always monotonically non-increasing. Nonetheless, for a given quantifier of the information contained in the system, it is in general not clear…
Quantum collision models allow for the dynamics of open quantum systems to be described by breaking the environment into small segments, typically consisting of non-interacting harmonic oscillators or two-level systems. This work introduces…
Understanding and predicting how complex systems respond to external perturbations is a central challenge in nonequilibrium statistical physics. Here we consider continuous-time Markov networks, which we subject to perturbations along a…
We present an intuitive, conceptual, but semi-rigorous introduction to the celebrated Markov Chain Monte Carlo method using a simple model of population dynamics as our motivation and focusing on a few elementary distributions.…
We consider finite-state time-nonhomogeneous Markov chains where the probability of moving from state $i$ to state $j\neq i$ at time $n$ is $G(i,j)/n^\zeta$ for a ``generator'' matrix $G$ and strength parameter $\zeta>0$. In these chains,…