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Based on a coupling approach, we prove uniform in time propagation of chaos for weakly interacting mean-field particle systems with possibly non-convex confinement and interaction potentials. The approach is based on a combination of…

Probability · Mathematics 2018-05-30 Alain Durmus , Andreas Eberle , Arnaud Guillin , Raphael Zimmer

Ensemble averages of the sensitivity to initial conditions $\xi(t)$ and the entropy production per unit time of a {\it new} family of one-dimensional dissipative maps, $x_{t+1}=1-ae^{-1/|x_t|^z}(z>0)$, and of the known logistic-like maps,…

Statistical Mechanics · Physics 2009-11-10 Garin F. J Ananos , Constantino Tsallis

We introduce the notion of dynamical metric order of a continuous map on a compact metric space, study its basic properties, and compute it for several classes of maps. This concept which is a counterpart of the metric mean dimension with…

Dynamical Systems · Mathematics 2026-04-14 Maria Carvalho , Fagner B. Rodrigues

The energy level statistics of uniform random graphs are studied, by treating the graphs as random tight-binding lattices. The inherent random geometry of the graphs and their dynamical spatial dimensionality, leads to various quantum…

Disordered Systems and Neural Networks · Physics 2024-12-20 Ioannis Kleftogiannis , Ilias Amanatidis

In 2016, Hou and Wang introduced the concept of multiple mappings based on iterated function system, which is an important branch of fractal theory. In this paper, we introduce the definitions of shadowing, average shadowing, transitive,…

Dynamical Systems · Mathematics 2023-11-07 Yingcui Zhao

A system of interacting particles described by stochastic differential equations is considered. As oppopsed to the usual model, where the noise perturbations acting on different particles are independent, here the particles are subject to…

Analysis of PDEs · Mathematics 2016-06-23 Michele Coghi , Franco Flandoli

This article is about the shadowing property of homeomorphisms on compact metric spaces and the map associating a point of the space to each pseudo-orbit, called 'shadowing map'. Based on some particular dynamical properties, as…

Dynamical Systems · Mathematics 2025-04-02 Alfonso Artigue

We compare three notions of genericity of separable metric structures. Our analysis provides a general model theoretic technique of showing that structures are generic in descriptive set theoretic (topological) sense and in measure…

Logic · Mathematics 2008-02-04 Alexander Usvyatsov

We investigate the spread complexity of a generic two-level subsystem of a larger system to analyze the influence of energy level statistics, comparing chaotic and integrable systems. Initially focusing on the nearest-neighbor level…

High Energy Physics - Theory · Physics 2025-04-28 Amin Faraji Astaneh , Niloofar Vardian

In this work, we prove the well-posedness and propagation of chaos for a stochastic particle system in mean-field interaction under the assumption that the interacting kernel belongs to a suitable $L_t^q-L_x^p$ space. Contrary to the large…

Probability · Mathematics 2023-07-19 Milica Tomašević

The aim of the paper is to correct and improve some results concerning distributional chaos of type 3. We show that in a general compact metric space, distributional chaos of type 3, denoted DC3, even when assuming the existence of an…

Dynamical Systems · Mathematics 2016-03-02 Jana Hantáková , Samuel Roth , Zuzana Roth

We consider the problems of chaos in disorder and temperature for coupled copies of the mixed p-spin models. Under certain assumptions on the parameters of the models we will first prove a weak form of chaos by showing that the overlap is…

Probability · Mathematics 2013-09-18 Wei-Kuo Chen , Dmitry Panchenko

The problem of formation of generic structures in the Universe is addressed, whereby first the kinematics of inertial continua for coherent initial data is considered. The generalization to self--gravitating continua is outlined focused on…

Astrophysics · Physics 2007-05-23 T. Buchert

We give sufficient conditions for sensitivity of continuous group actions on uniform spaces.

Dynamical Systems · Mathematics 2013-02-06 Tullio Ceccherini-Silberstein , Michel Coornaert

Inspired by recent work of Alberts, Khanin and Quastel, we formulate general conditions ensuring that a sequence of multi-linear polynomials of independent random variables (called polynomial chaos expansions) converges to a limiting random…

Probability · Mathematics 2016-10-26 Francesco Caravenna , Rongfeng Sun , Nikos Zygouras

We numerically investigate the long--time evolution of density perturbations after the first appearance of caustics in an expanding cosmological model with one--dimensional `single--wave' initial conditions. Focussing on the time--intervals…

Astrophysics · Physics 2007-05-23 Taihei Yano , Hiroko Koyama , Thomas Buchert , Naoteru Gouda

We extend the concept of generalized synchronization of chaos, a phenomenon that occurs in driven dynamical systems, to the context of autonomous spatiotemporal systems. It means a situation where the chaotic state variables in an…

Chaotic Dynamics · Physics 2009-11-13 O. Alvarez-Llamoza , M. G. Cosenza

The propagation of chaos is a central concept of kinetic theory that serves to relate the equations of Boltzmann and Vlasov to the dynamics of many-particle systems. Propagation of chaos means that molecular chaos, i.e., the stochastic…

Probability · Mathematics 2007-05-23 Alexander David Gottlieb

This paper investigates a natural generalization of the kappa-mu fading channel in which the line-of-sight (LOS) component is subject to shadowing. This fading distribution has a clear physical interpretation, good analytical properties and…

Information Theory · Computer Science 2024-10-30 J. F. Paris

In this paper, we investigate the distributional chaos of the composition operator $T_{\varphi}:f\mapsto f\circ\varphi$ on $L^{p}(X,\mathcal{B},\mu)$, $1\leq p <\infty$. We provide a characterization and practical sufficient conditions on…

Functional Analysis · Mathematics 2025-03-04 Shengnan He , Zongbin Yin