Related papers: Fluctuation bounds for chaos plus noise in dynamic…
The weak noise limit of dissipative dynamical systems is often the most fascinating one. In such a case fluctuations can interact with a rich complexity frequently hidden in deterministic systems to give rise of completely new phenomena…
Here we review and extend central limit theorems for highly chaotic but deterministic semi-dynamical discrete time systems. We then apply these results show how Brownian motion-like results are recovered, and how an Ornstein-Uhlenbeck…
We study the fluctuation properties of a one-dimensional many-body quantum system composed of interacting bosons, and investigate the regimes where quantum noise or, respectively, thermal excitations are dominant. For the latter we develop…
Turbulence, namely, irregular fluctuations in space and time characterize fluid flows in general and atmospheric flows in particular.The irregular,i.e., nonlinear space-time fluctuations on all scales contribute to the unpredictable nature…
The propagation of chaos and associated law of large numbers for mean-field interacting age-dependent Hawkes processes (when the number of processes n goes to +$\infty$) being granted by the study performed in (Chevallier, 2015), the aim of…
Periodically kicked Floquet systems such as the kicked rotor are a paradigmatic and illustrative simple model of chaos. For non-integrable quantum dynamics there are several diagnostic measures of the presence of (or the transition to)…
In a vast area of probabilistic limit theorems for dynamical systems with chaotic behaviors always only functional form (exponential, power, etc) of the asymptotic laws and of convergence rates were studied. However, for basically all…
This paper establishes some criteria of chaos in non-autonomous discrete systems. Several criteria of strong Li-Yorke chaos are given. Based on these results, some criteria of distributional chaos in a sequence are established. Moreover,…
We provide a stochastic interpretation of non-commutative Dirichlet forms in the context of quantum filtering. For stochastic processes motivated by quantum optics experiments, we derive an optimal finite time deviation bound expressed in…
For many externally driven complex systems neither the noisy driving force, nor the internal dynamics are a priori known. Here we focus on systems for which the time dependent activity of a large number of components can be monitored,…
In systems removed from equilibrium, intrinsic microscopic fluctuations become correlated over distances comparable to the characteristic macroscopic length over which the external constraint is exerted. In order to investigate this…
Noisy fluctuations are ubiquitous in complex systems. They play a crucial or delicate role in the dynamical evolution of gene regulation, signal transduction, biochemical reactions, among other systems. Therefore, it is essential to…
An investigation of the mesoscopic dynamics of chemical systems whose mass action equation gives rise to a deterministic chaotic attractor is carried out. A reactive lattice-gas model for the three-variable autocatalator is used to provide…
The chaotic hypothesis has several implications which have generated interest in the literature because of their generality and because a few exact predictions are among them. However its application to Physics problems requires attention…
We consider a purely harmonic chain of oscillators which is perturbed by a stochastic noise. Under this perturbation, the system exhibits two conserved quantities: the volume and the energy. At the level of the hydrodynamic limit, under…
The fluctuation in electric current in nonequilibrium steady states is investigated by molecular dynamics simulation of macroscopically uniform conductors. At low frequencies, appropriate decomposition of the spectral intensity of current…
The complex spatiotemporal patterns of atmospheric flows resulting from the cooperative existence of fluctuations ranging in size from millimeters to thousands of kilometers are found to exhibit long-range spatial and temporal correlations…
We conjecture that the current fluctuations in one-dimensional driven transport systems obey an upper bound determined by the mean current and the driving force. This inequality originates from repulsive interactions between transporting…
These lecture notes give a short review of methods such as the matrix ansatz, the additivity principle or the macroscopic fluctuation theory, developed recently in the theory of non-equilibrium phenomena. They show how these methods allow…
The dynamics of one species chemical kinetics is studied. Chemical reactions are modelled by means of continuous time Markov processes whose probability distribution obeys a suitable master equation. A large deviation theory is formally…