Related papers: Anomalous diffusion in run-and-tumble motion
{\it E. coli} bacteria swim in straight runs interrupted by sudden reorientation events called tumbles. The resulting random walks give rise to density fluctuations that can be derived analytically in the limit of non interacting particles…
A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…
Random walks as well as diffusions in random media are considered. Methods are developed that allow one to establish large deviation results for both the `quenched' and the `averaged' case.
The movement of organisms and cells can be governed by occasional long distance runs, according to an approximate L\'evy walk. For T cells migrating through chronically-infected brain tissue, runs are further interrupted by long pauses, and…
Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a…
Anomalous transport in a circular comb is considered. The circular motion takes place for a fixed radius, while radii are continuously distributed along the circle. Two scenarios of the anomalous transport, related to the reflecting and…
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 consider random walks in dynamic random environments given by Markovian dynamics on $\mathbb{Z}^d$. We assume that the environment has a stationary distribution $\mu$ and satisfies the Poincar\'e inequality w.r.t. $\mu$. The random walk…
We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process,…
We propose a variety of models of random walk, discrete in space and time, suitable for simulating stable random variables of arbitrary index $\alpha$ ($0< \alpha \le 2$), in the symmetric case. We show that by properly scaled transition to…
We introduce the pushy random walk, where a walker can push multiple obstacles, thereby penetrating large distances in environments with finite obstacle density. This process provides a minimal model for experimentally observed interactions…
Brownian motion is a foundational physical process characterized by a mean squared displacement that scales linearly in time in thermal equilibrium, known as diffusion. At short times, the mean squared displacement becomes ballistic,…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
In this paper we study subdiffusion in a system with a thin membrane. At the beginning, the random walk of a particle is considered in a system with a discrete time and space variable and then the probability describing the evolution of the…
We are concerned with random walks on $\mathbb{Z}^d$, $d\geq 3$, in an i.i.d. random environment with transition probabilities $\epsilon$-close to those of simple random walk. We assume that the environment is balanced in one fixed…
In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm was already introduced in both the Brownian context and in the Ornstein-Uhlenbeck context. Here…
For spatially one-dimensional run-and-tumble dynamics with mass conservation we develop a coarse phase diagram, that discriminates between global decay to equidistributed constant states, existence of spatially non-trivial waves, and finite…
Understanding flow and transport of bacteria in porous media is crucial to technologies such as bioremediation, biomineralization or enhanced oil recovery. While physicochemical bacteria filtration is well-documented, recent studies showed…
Starting with a percolation model in $\Z^d$ in the subcritical regime, we consider a random walk described as follows: the probability of transition from $x$ to $y$ is proportional to some function $f$ of the size of the cluster of $y$.…
We study the long-time behaviour of a run and tumble model which is a kinetic-transport equation describing bacterial movement under the effect of a chemical stimulus. The experiments suggest that the non-uniform tumbling kernels are…