Related papers: Scaling limits of additive functionals of interact…

An ensemble of classical subsystems interacting with surrounding particles has been considered. In general case, a phase volume of the subsystems ensemble was shown to be a function of time. The evolutional equations of the ensemble are…

We consider general stochastic systems of interacting particles with noise which are relevant as models for the collective behavior of animals, and rigorously prove that in the mean-field limit the system is close to the solution of a…

We construct marked Gibbs point processes in $\mathbb{R}^d$ under quite general assumptions. Firstly, we allow for interaction functionals that may be unbounded and whose range is not assumed to be uniformly bounded. Indeed, our typical…

We prove central limit theorems for additive functionals of stationary fields under integrability conditions on the higher-order spectral densities, which are derived using the Holder-Young-Brascamp-Lieb inequality.

We consider a particle system with weights and the scaling limits derived from its occupation time. We let the particles perform independent recurrent L\'evy motions and we assume that their initial positions and weights are given by a…

A system of stochastic differential equations for the velocity and density of a classical self-gravitating matter is investigated by means of the field theoretic renormalization group. The existence of two types of large-scale scaling…

In the present work, it is developed a formalism to deal with the macroscopic study of the astrophysical systems, which is based on the consideration of the exponential self-similarity scaling laws that these systems exhibit during the…

In this paper we consider an interacting particle system modeled as a system of $N$ stochastic differential equations driven by Brownian motions with a drift term including a confining potential acting on each particle, and an interaction…

We consider a classical system of n charged particles in an external confining potential, in any dimension d larger than 2. The particles interact via pairwise repulsive Coulomb forces and the coupling parameter scales like the inverse of n…

A stochastic dynamics $({\bf X}(t))_{t\ge0}$ of a classical continuous system is a stochastic process which takes values in the space $\Gamma$ of all locally finite subsets (configurations) in $\Bbb R$ and which has a Gibbs measure $\mu$ as…

In various fields from quantum physics to biology, the open quantum dynamics of a system consisting of interacting subsystems emphasizes its fundamental functionality. The local approach, deriving a dissipator in a master equation by…

In this paper we give a new proof of the second order Boltzmann-Gibbs principle. The proof does not impose the knowledge on the spectral gap inequality for the underlying model and it relies on a proper decomposition of the antisymmetric…

Many self-gravitating systems often show scaling properties in their mass density, system size, velocities and so on. In order to clarify the origin of these scaling properties, we consider the stationary state of N-body system with inverse…

We analyze the stochastic scaling laws arising in the invicid limit of the decaying solutions of the Burgers equation. The linear scaling of the velocity structure functions is shown to reflect the domination by shocks of the long-time…

We consider irreversible translation-invariant interacting particle systems on the $d$-dimensional cubic lattice with finite local state space, which admit at least one Gibbs measure as a time-stationary measure. Under some mild degeneracy…

We investigate propagation of perturbations of equilibrium states for a wide class of 1D interacting particle systems. The class of systems considered incorporates zero range, $K$-exclusion, mysanthropic, `bricklayers' models, and much…

We study scaling limits of nonlinear functions $G$ of random grain model $X$ on $\mathbb{R}^d $ with long-range dependence and marginal Poisson distribution. Following Kaj et al (2007) we assume that the intensity $M$ of the underlying…

In this paper we prove the convergence of a suitable particle system towards the BGK model. More precisely, we consider an interacting stochastic particle system in which each particle can instantaneously thermalize locally. We show that,…

We propose a general approach, named by us hyperstatistics, to treat complex systems, in which Boltzmann-Gibbs statistics breaks down in domains of the system. Hyperstatistics preserves the concavity of nonadditive $q$-entropy. We obtain…

We generalize the usual exponential Boltzmann factor to any reasonable and potentially observable distribution function, $B(E)$. By defining generalized logarithms $\Lambda$ as inverses of these distribution functions, we are led to a…