Related papers: Stochastic averaging for a spatial population mode…
We propose a class of non-Markov population models with continuous or discrete state space via a limiting procedure involving sequences of rescaled and randomly time-changed Galton--Watson processes. The class includes as specific cases the…
Deterministic models of vegetation often summarize, at a macroscopic scale, a multitude of intrinsically random events occurring at a microscopic scale. We bridge the gap between these scales by demonstrating convergence to a mean-field…
For boundary-driven non-equilibrium Markov models of non-interacting particles in one dimension, either in continuous space with the Fokker-Planck dynamics involving an arbitrary force $F(x)$ and an arbitrary diffusion coefficient $D(x)$,…
We investigate systems of self-propelled particles with alignment interaction. Compared to previous work, the force acting on the particles is not normalized and this modification gives rise to phase transitions from disordered states at…
We develop a semi-parametric state-space model for time-series data with latent regime transitions. Classical Markov-switching models use fixed parametric transition functions, such as logistic or probit links, which restrict flexibility…
We consider a self-gravitating collisionless gas as described by the Vlasov-Poisson or Einstein-Vlasov system or a self-gravitating fluid ball as described by the Euler-Poisson or Einstein-Euler system. We give a simple proof for the finite…
We define non-Markovian quantum dynamics as evolution in which the current state depends on all past states, and completely characterize its structure under the assumptions of complete positivity and non-signalling. The resulting…
Understanding the fluctuations by which phenomenological evolution equations with thermodynamic structure can be enhanced is the key to a general framework of nonequilibrium statistical mechanics. These fluctuations provide an idealized…
We construct two types of equilibrium dynamics of infinite particle systems in a locally compact Polish space $X$, for which certain fermion point processes are invariant. The Glauber dynamics is a birth-and-death process in $X$, while in…
We consider a Vlasov-Fokker-Planck equation governing the evolution of the density of interacting and diffusive matter in the space of positions and velocities. We use a probabilistic interpretation to obtain convergence towards equilibrium…
In this paper we derive an extra class of non-Markovian master equations where the system state is written as a sum of auxiliary matrixes whose evolution involve Lindblad contributions with local coupling between all of them, resembling the…
We study the dynamics of inertial particles in turbulence using datasets obtained from both direct numerical simulations and laboratory experiments of turbulent swirling flows. By analyzing time series of particle velocity increments at…
We study a system of $N$ interacting particles on $\bf{Z}$. The stochastic dynamics consists of two components: a free motion of each particle (independent random walks) and a pair-wise interaction between particles. The interaction belongs…
We model evolution according to an asymmetric game as occurring in multiple finite populations, one for each role in the game, and study the effect of subjecting individuals to stochastic strategy mutations. We show that, when these…
We discuss several models of the dynamics of interacting populations. The models are constructed by nonlinear differential equations and have two sets of parameters: growth rates and coefficients of interaction between populations. We…
Growth in static and controlled environments such as a Petri dish can be used to study the spatial population dynamics of microorganisms. However, natural populations such as marine microbes experience fluid advection and often grow up in…
In recent years, there has been tremendous focus on identifying whether effective descriptions of open quantum systems such as master equations, can accurately describe the dynamics of open quantum systems. One particular question is…
There are many processes in cell biology that can be modelled in terms of an actively switching particle. The continuous degrees of freedom evolve according to a hybrid stochastic differential equation (hSDE) whose drift term depends on a…
Biological systems are typically highly open, non-equilibrium systems that are very challenging to understand from a statistical mechanics perspective. While statistical treatments of evolutionary biological systems have a long and rich…
A possible approach to description of the non equilibrium system has been proposed. Based on the Fokker-Plank equation in term of energy for non equilibrium distribution function of macroscopical system was obtained the stationary solution…