Related papers: The Local Time Distribution of a Particle Diffusin…
Non-Gaussian diffusion was recently observed in gas mixtures with mass and fraction contrast [F. Nakai et al, Phys. Rev. E 107, 014605 (2023)]. The mean square displacement of a minor gas particle with a small mass is linear in time, while…
We present a model of anomalous diffusion consisting of an ensemble of particles undergoing homogeneous Brownian motion except for confinement by randomly placed reflecting boundaries. For power-law distributed compartment sizes, we…
A possible mechanism leading to anomalous diffusion is the presence of long-range correlations in time between the displacements of the particles. Fractional Brownian motion, a non-Markovian self-similar Gaussian process with stationary…
We study the biased diffusion of particles moving in one direction under the action of a constant force in the presence of a piecewise linear random potential. Using the overdamped equation of motion, we represent the first and second…
We study asymptotic properties of the system of interacting diffusion particles on the real line which transfer a mass [arXiv:1408.0628]. The system is a natural generalization of the coalescing Brownian motions. The main difference is that…
It is well known that on long time scales the behaviour of tracer particles diffusing in a cellular flow is effectively that of a Brownian motion. This paper studies the behaviour on "intermediate" time scales before diffusion sets in.…
We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of the Brownian motion arise in the study of electronic transport in weakly…
Large unweighted directed graphs are commonly used to capture relations between entities. A fundamental problem in the analysis of such networks is to properly define the similarity or dissimilarity between any two vertices. Despite the…
According to the classical theory of Brownian motion, the mean squared displacement of diffusing particles evolves linearly with time whereas the distribution of their displacements is Gaussian. However, recent experiments on mesoscopic…
It has been observed in numerous experiments, simulations, and various theoretical treatments that the spreading of particles can be modeled by the continuous-time random walk. We consider two well-known cases, i.e., Gaussian displacements…
The fundamental solutions of diffusion equation for the local-equilibrium and nonlocal models are considered as the limiting cases of the solution of a problem related to consideration of the Brownian particles random walks. The differences…
Stochastic motion of particles in a highly unstable potential generates a number of diverging trajectories leading to undefined statistical moments of the particle position. This makes experiments challenging and breaks down a standard…
How long does a diffusing molecule spend in a close vicinity of a confining boundary or a catalytic surface? This quantity is determined by the boundary local time, which plays thus a crucial role in the description of various…
Area fluctuations of a Brownian excursion are described by the Airy distribution, which found applications in different areas of physics, mathematics and computer science. Here we generalize this distribution to describe the area…
This article deals with transport properties of one dimensional Brownian diffusion under the influence of a correlated quenched random force, distributed as a two-level Poisson process. We find in particular that large time scaling laws of…
We consider a system of non-interacting Brownian particles on a line with a step-like initial condition, and we investigate the behavior of the local time at the origin at large times. We compute the mean and the variance of the local time,…
This article addresses a modification of local time for stochastic processes, to be referred to as `natural local time'. It is prompted by theoretical developments arising in mathematical treatments of recent experiments and observations of…
We investigate fast diffusions on finite directed graphs. We prove results in a way dual to presented in Bobrowski, A. Ann. Henri Poincar\'e (2012) 13(6): 1501-1510 and Bobrowski, A., Morawska, K. DCDS-B (2012), 17(7): 2313-2327, and obtain…
We consider the problem of leakage or effusion of an ensemble of independent stochastic processes from a region where they are initially randomly distributed. The case of Brownian motion, initially confined to the left half line with…
Continuous-time random walks offer powerful coarse-grained descriptions of transport processes. We here microscopically derive such a model for a Brownian particle diffusing in a deep periodic potential. We determine both the waiting-time…