Related papers: Static large deviations for a reaction-diffusion m…
The input/output stability of an interconnected system composed of an ordinary differential equation and a damped string equation is studied. Issued from the literature on time-delay systems, an exact stability result is firstly derived…
Large deviations principles characterize the exponential decay rates of the probabilities of rare events. Cerrai and Rockner [13] proved that systems of stochastic reaction-diffusion equations satisfy a large deviations principle that is…
We obtain large deviations for a class of dependent random variables in the domain of attraction of an $\alpha$-stable law, $\alpha\in (0, 1)\cup (1, 2]$. This class includes ergodic sums of observables in the domain of attraction of an…
We consider the one dimensional asymmetric exclusion process with particle injection and extraction at two boundaries. The model is known to exhibit four distinct phases in its stationary state. We analyze the current statistics at the…
We consider two Ito equations that evolve on different time scales. The equations are fully coupled in the sense that all coefficients may depend on both the "slow" and the "fast" processes and the diffusion terms may be correlated. The…
Consider a one-dimensional shift-invariant attractive spin-flip system in equilibrium, constituting a dynamic random environment, together with a nearest-neighbor random walk that on occupied sites has a local drift to the right but on…
Systems consisting of a single ordinary differential equation coupled with one reaction-diffusion equation in a bounded domain and with the Neumann boundary conditions are studied in the case of particular nonlinearities from the…
We establish a large deviation principle for time dependent trajectories (paths) of the empirical density of $N$ particles with long range interactions, for homogeneous systems. This result extends the classical kinetic theory that leads to…
In this paper we study the long time dynamics of the solutions to the initial-boundary value problem for a scalar conservation law with a saturating nonlinear diffusion. After discussing the existence of a unique stationary solution and its…
Dynamics of many-body Hamiltonian systems with long range interactions is studied, in the context of the so called $\alpha-$HMF model. Building on the analogy with the related mean field model, we construct stationary states of the…
We prove the existence of solutions to a non-linear, non-local, degenerate equation which was previously derived as the formal hydrodynamic limit of an active Brownian particle system, where the particles are endowed with a position and an…
We study the emergence of typicality in classical systems with a large number of binary state variables. We show analytically that for sufficiently large subsets of the complete state space, state functions which can be associated with…
We investigate the stationary states of one-dimensional driven diffusive systems, coupled to boundary reservoirs with fixed particle densities. We argue that the generic phase diagram is governed by an extremal principle for the macroscopic…
We give a short analytic proof of local large deviations for i.i.d. random variables in the domain of a multivariate $\alpha$-stable law, $\alpha\in(0,1)\cup(1,2]$. Our method simultaneously covers lattice and nonlattice distributions (and…
We propose a computational method for large deviation statistics of time-averaged quantities in general Markov processes. In our proposed method, we repeat a response measurement against external forces, where the forces are determined by…
We obtain error rates for large deviations of sums of i.i.d. random variables in, a particular case, of the domain of a non-symmetric infinite mean $\alpha=1$-stable law. The focus of this work is on the method of proof via analytic…
We experimentally investigate the statistical behaviour of a model two-dimensional granular system undergoing stationary sedimentation. Buoyant cylindrical particles are rotated in liquid-filled drum, thus confined in a harmonic centripetal…
We investigate the large population dynamics of a family of stochastic particle systems with three-state cyclic individual behaviour and parameter-dependent transition rates. On short time scales, the dynamics turns out to be approximated…
We prove hydrostatics of boundary driven gradient exclusion processes, Fick's law and we present a simple proof of the dynamical large deviations principle which holds in any dimension
Large time dynamics of reaction-diffusion systems modeling some irreversible reaction networks are investigated. Depending on initial masses, these networks possibly possess boundary equilibria, where some of the chemical concentrations are…