Diffusion of particles in random, correlated diffusivity landscapes can serve as one of the models leading to the so-called Brownian yet non-Gaussian diffusion. Under the corresponding choice of parameters, the model leads to the mean squared displacement of particles growing linearly in time, with the probability density function (PDF) of displacements changing its shape from a double-sided...
We study the statistics of a one-dimensional randomly advected field with diffusion. The motivation for this setup comes from a straightforward interpretation as advection of particles in one-dimensional turbulence, but it is also related to a problem of synchronization of dynamical systems driven by common noise. A general class of lattice models describing the joint effect of random...
The study of the dynamics of occupation time has a variety of applications. For ex-
ample, it has been used to analyze the morphological dynamics of interfaces, analysis
of the fluorescence intermittency emitting from colloidal semiconductor dots, optical
imaging etc to name a few. The occupation time dynamics have been studied for
numerous problems in the context of non-equilibrium...
