Related papers: On stochastic perturbations of slowly changing dyn…
In this paper we develop a metastability theory for a class of stochastic reaction-diffusion equations exposed to small multiplicative noise. We consider the case where the unperturbed reaction-diffusion equation features multiple…
The exit problem for small perturbations of a dynamical system in a domain is considered. It is assumed that the unperturbed dynamical system and the domain satisfy the Levinson conditions. We assume that the random perturbation affects the…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
We calculate the explicit probability distribution function for the flux between sites in a simple discrete time diffusive system composed of independent random walkers. We highlight some of the features of the distribution and we discuss…
The diffusive epidemic process is a paradigmatic example of an absorbing state phase transition in which healthy and infected individuals spread with different diffusion constants. Using stochastic activity spreading simulations in…
Stationary distributions of multivariate diffusion processes have recently been proposed as probabilistic models of causal systems in statistics and machine learning. Motivated by these developments, we study stationary multivariate…
We provide an explicit rigorous derivation of a diffusion limit - a stochastic differential equation with additive noise - from a deterministic skew-product flow. This flow is assumed to exhibit time-scale separation and has the form of a…
Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe the long time behavior of the particle,…
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
This paper studies the limit of a kinetic evolution equation involving a small parameter and driven by a random process which also scales with the small parameter. In order to prove the convergence in distribution to the solution of a…
In this paper, we study a stochastically driven non-equilibrium quantum system where the driving protocols consist of hopping and waiting processes. The waiting times between two hopping processes satisfy a heavy-tailed distribution. By…
We study the probability distribution of a current flowing through a diffusive system connected to a pair of reservoirs at its two ends. Sufficient conditions for the occurrence of a host of possible phase transitions both in and out of…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
Stochastic homogenization is achieved for a class of elliptic and parabolic equations describing the lifetime, in large domains, of stationary diffusion processes in random environment which are small, statistically isotropic perturbations…
A dynamical system perturbed by white noise in a neighborhood of an unstable fixed point is considered. We obtain the exit asymptotics in the limit of vanishing noise intensity. This is a refinement of a result by Kifer (1981).
We consider fluctuations of the time-averaged current in the one-dimensional weakly-asymmetric exclusion process on a ring. The optimal density profile which sustains a given fluctuation exhibits an instability for low enough currents,…
We study the influence of a dissipation process on diffusion dynamics triggered by fluctuations with long-range correlations. We make the assumption that the perturbation process involved is of the same kind as those recently studied…
Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…