Related papers: Ergodicity and Central Limit Theorem in Systems wi…
We consider a class of mechanical particle systems interacting with thermostats. Particles move freely between collisions with disk-shaped thermostats arranged periodically on the torus. Upon collision, an energy exchange occurs, in which a…
We study the ergodic properties of a two-dimensional self-gravitating system using molecular dynamics simulations. We apply three different tests for ergodicity: a direct method comparing the time average of a particle momentum and position…
Isolated long-range interacting particle systems appear generically to relax to non-equilibrium states ("quasi-stationary states" or QSS) which are stationary in the thermodynamic limit. A fundamental open question concerns the "robustness"…
This work explores fundamental statistical and thermodynamic properties of short-and long-range-interacting systems. The purpose of this study is twofold. Firstly, we rigorously prove that the probability distribution of arbitrary few-body…
Using numerical simulations we studied the long time relaxation of the hopping conductivity. Even though no modern computation is able to simulate the behavior of a large size system over minutes or hours so as to observe the relaxation,…
We prove a central limit theorem for network formation models with strategic interactions and homophilous agents. Since data often consists of observations on a single large network, we consider an asymptotic framework in which the network…
In this paper, we provide relations among the following properties: (a) the tail triviality of a probability measure $\mu$ on the configuration space ${\boldsymbol\Upsilon}$; (b) the finiteness of the $L^2$-transportation-type distance…
Systems with long range interactions display some anomalies when its dynamics and thermodynamics are studied below certain conditions. Among these anomalies are the quasi- stationary states, which are exacerbated because of special initial…
The Ising model with ferromagnetic interactions that decay as $1/r^\alpha$ is analyzed in the non-extensive regime $0\leq\alpha\leq d$, where the thermodynamic limit is not defined. In order to study the asymptotic properties of the model…
Motivated by recent experiments with ultra-cold matter, we derive a new bound on the propagation of information in $D$-dimensional lattice models exhibiting $1/r^{\alpha}$ interactions with $\alpha>D$. The bound contains two terms: One…
A finite quantum system evolving unitarily equilibrates in a probabilistic fashion. In the general many-body setting the time-fluctuations of an observable \mathcal{A} are typically exponentially small in the system size. We consider here…
The question of deriving general force/flux relationships that apply out of the linear response regime is a central topic of theories for nonequilibrium statistical mechanics. This work applies an information theory perspective to compute…
We consider the behavior of an interacting many particle system under slow external driving -- a many body generalization of the Landau-Zener paradigm. We find that a conspiracy of interactions and driving leads to physics profoundly…
It is shown that a recently proposed model for the gravitational interaction in non relativistic quantum mechanics is the instantaneous action at a distance limit of a field theoretic model containing a negative energy field. It reduces to…
Realistic effective interparticle interactions of quantum many-body systems are widely seen as being short-range. However, the rigorous mathematical analysis of this type of model turns out to be extremely difficult, in general, with many…
For a classical system with long-range interactions, a soft mode exists whenever a stationary state spontaneously breaks a continuous symmetry of the Hamiltonian. Besides that, if the corresponding coordinate associated to the symmetry…
Limit theorems are proved for quadratic forms of Gaussian random fields in presence of long memory. We obtain a non central limit theorem under a minimal integrability condition, which allows isotropic and anisotropic models. We apply our…
A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain conditional $\alpha$-mixing…
Dynamical systems with $\epsilon$ small random perturbations appear in both continuous mechanical motions and discrete stochastic chemical kinetics. The present work provides a detailed analysis of the central limit theorem (CLT), with a…
Understanding the behaviors of ecological systems is challenging given their multi-faceted complexity. To proceed, theoretical models such as Lotka-Volterra dynamics with random interactions have been investigated by the dynamical…