Related papers: Dynamical mean-field approximations for a diffusiv…
We investigate the mean-field limit for interacting particle systems through a duality-based framework and obtain quantitative estimates on the convergence of marginals as well as on correlation functions. In particular, for merely…
We investigate the generalized contact process with two absorbing states in one space dimension by means of large-scale Monte-Carlo simulations. Treating the creation rate of active sites between inactive domains as an independent parameter…
A broad class of systems, including ecological, epidemiological, and sociological ones, are characterized by populations of individuals assigned to specific categories, e.g., a chemical species, an opinion or an epidemic state, that are…
Recently, diagrammatic extensions of dynamical mean field theory (DMFT) have been proposed for including short- and long-range correlations beyond DMFT on an equal footing. We employ one of these, the dynamical vertex approximation…
Motivated by considerations from neuroscience (macroscopic behavior of large ensembles of interacting neurons), we consider a population of mean field interacting diffusions in $\mathbf {R}^m$ in the presence of a random environment and…
This paper studies a general class of stochastic population processes in which agents interact with one another over a network. Agents update their behaviors in a random and decentralized manner according to a policy that depends only on…
We examine a model in which a nonequilibrium phase transition from an active to an extinct state is observed. The order of this phase transition has been shown to be either continuous or first-order, depending on the parameter values and…
We study the random connection model on hyperbolic space $\mathbb{H}^d$ in dimension $d=2,3$. Vertices of the spatial random graph are given as a Poisson point process with intensity $\lambda>0$. Upon variation of $\lambda$ there is a…
We provide a review of recently-develop dynamical mean-field theory (DMFT) approaches to the general problem of strongly correlated electronic systems with disorder. We first describe the standard DMFT approach, which is exact in the limit…
We study the stationary properties of the two-dimensional pair contact process, a nonequilibrium lattice model exhibiting a phase transition to an absorbing state with an infinite number of configurations. The critical probability and…
Although real-world complex systems typically interact through sparse and heterogeneous networks, analytic solutions of their dynamics are limited to models with all-to-all interactions. Here, we solve the dynamics of a broad range of…
The objective of this article is to analyse the statistical behaviour of a large number of weakly interacting diffusion processes evolving under the influence of a periodic interaction potential. We focus our attention on the combined mean…
The paper is concerned with the approximation of the deterministic the mean field type control system by a mean field Markov chain. It turns out that the dynamics of the distribution in the approximating system is described by a system of…
Many complex dynamical systems in the real world, including ecological, climate, financial, and power-grid systems, often show critical transitions, or tipping points, in which the system's dynamics suddenly transit into a qualitatively…
The steady-state phase diagram of the one-dimensional reaction-diffusion model 2A -> 3A, 2A -> 0 is studied through the non-hermitian density matrix renormalization group. In the absence of single-particle diffusion the model reduces to the…
Communication between single cells or higher organisms by means of diffusive compounds is an important phenomenon in biological systems. Modelling therefore often occurs, most straightforwardly by a diffusion equation with suitable flux…
Computer simulations of the phenomenon of contact melting in binary alloys with chemical miscibility gap are performed on the basis of the phase field theory. Kinetics of the process is examined within the isothermal approximation, as a…
Cluster dynamical mean field and maximum entropy analytical continuation methods are used to obtain theoretical estimates for the many-body density of states, electron self-energy, in-plane and c-axis optical conductivity and the $B_{1g}$…
An effective medium approach similar to the coherent potential approximation (CPA) in the theory of disordered alloys and to the DMFT has been extended to the renormalization group equations in the local potential approximation (LPA).…
The dynamic behaviour of stochastic spreading processes on a network model based on k-regular graphs is investigated. The contact process and the susceptible-infected-susceptible model for the spread of epidemics are considered as prototype…