Related papers: Single file dynamics of tethered random walkers
The one-dimensional symmetric exclusion process, the simplest interacting particle process, is a lattice-gas made of particles that hop symmetrically on a discrete line respecting hard-core exclusion. The system is prepared on the infinite…
We study the long-time behavior of the probability density associated with the decoupled continuous-time random walk which is characterized by a superheavy-tailed distribution of waiting times. It is shown that if the random walk is…
We consider three kinds of discrete-time arrival processes: transient, intermediate and recurrent, characterized by a finite, possibly finite and infinite number of events, respectively. In this context, we study renewal processes which are…
One-dimensional movement of interacting particles is a challenging problem where the correlation between particles induces non-trivial collective effects. In contrast to the single-file diffusion case, the pure ballistic single file…
We present the results of a numerical investigation of charged-particle transport across a synthesized magnetic configuration composed of a constant homogeneous background field and a multiscale perturbation component simulating an effect…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
We study the dynamics of a one-dimensional run and tumble particle subjected to confining potentials of the type $V(x) = \alpha \, |x|^p$, with $p>0$. The noise that drives the particle dynamics is telegraphic and alternates between $\pm 1$…
We study single-file diffusion on a one-dimensional lattice with a random fractal distribution of hopping rates. For finite lattices, this problem shows three clearly different regimes, namely, nearly independent particles, highly…
Tracer diffusion in single-file systems, where particles are restricted to move on a line without passing each other, has been a fertile ground to investigate anomalous diffusion and strong memory effects. While the long-time behavior of…
We investigate the diffusive motion of an overdamped classical particle in a 1D random potential using the mean first-passage time formalism and demonstrate the efficiency of this method in the investigation of the large-time dynamics of…
We consider a basic one-dimensional model of diffusion which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of the per-site trapping time. This model is closely related to the continuous time random…
We study diffusion of (fluorescently) tagged hard-core interacting particles of finite size in a finite one-dimensional system. We find an exact analytical expression for the tagged particle probability density using a coordinate…
We consider a discrete time random walk in one dimension. At each time step the walker jumps by a random distance, independent from step to step, drawn from an arbitrary symmetric density function. We show that the expected positive maximum…
The goal of this note is to prove a law of large numbers for the empirical speed of a green particle that performs a random walk on top of a field of red particles which themselves perform independent simple random walks on $\Z^d$, $d \geq…
We introduce a model of interacting Random Walk, whose hopping amplitude depends on the number of walkers/particles on the link. The mesoscopic counterpart of such a microscopic dynamics is a diffusing system whose diffusivity depends on…
We study how the order of N independent random walks in one dimension evolves with time. Our focus is statistical properties of the inversion number m, defined as the number of pairs that are out of sort with respect to the initial…
Single-file diffusion refers to the motion in narrow channels of particles which cannot bypass each other. These strong correlations between particles lead to tracer subdiffusion, which has been observed in contexts as varied as transport…
Single-file transport refers to the motion of particles in a narrow channel, such that they cannot bypass each other. This constraint leads to strong correlations between the particles, described by correlation profiles, which measure the…
We study the dynamics of a single inertial run-and-tumble particle on a straight line. The motion of this particle is characterized by two intrinsic time-scales, namely, an inertial and an active time-scale. We show that interplay of these…
Interacting particles diffusing in single-file is a fundamental model of transport in narrow channels where particles cannot bypass each other. An important result has been obtained by Kollmann [Phys. Rev. Lett. 90, 180602 (2003)] for the…