Related papers: Run-and-tumble motion with step-like responses to …
The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that…
The statistics of records for a time series generated by a continuous time random walk is studied, and found to be independent of the details of the jump length distribution, as long as the latter is continuous and symmetric. However, the…
The movement of organisms is subject to a multitude of influences of widely varying character: from the bio-mechanics of the individual, over the interaction with the complex environment many animals live in, to evolutionary pressure and…
We study active particles performing independent run and tumble motion on an infinite line with velocities $v_0 \sigma(t)$, where $\sigma(t) = \pm 1$ is a dichotomous telegraphic noise with constant flipping rate $\gamma$. We first consider…
We consider random walks with finite second moment which drifts to $-\infty$ and have heavy tail. We focus on the events when the minimum and the final value of this walk belong to some compact set. We first specify the associated…
Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walks are proving to be effective simulators of such phenomena. Here we report the realization of a…
Time delay in general leads to instability in some systems, while a specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a non-stationary stochastic…
A transition of quantum walk induced by classical randomness changes the probability distribution of the walker from a two-peak structure to a single-peak one when the random parameter exceeds a critical value. We first establish the…
In the chemotactic motion of Escherichia coli, the switching of transmembrane chemoreceptors between active and inactive states is one of the most important steps of the signaling pathway. We study the effect of this switching time-scale on…
We present a methodology for the study of the dispersion of trajectories of stochastic processes in reconstructed phase spaces from observed data. The methodology allows to find ensembles of analog states, i.e. states that are close in the…
Complex or hostile environments can sometimes inhibit the movement capabilities of diffusive particles or active swimmers, who may thus become stuck in fixed positions. This occurs, for example, in the adhesion of bacteria to surfaces at…
We consider a Markov jump process on a general state space to which we apply a time-dependent weak perturbation over a finite time interval. By martingale-based stochastic calculus, under a suitable exponential moment bound for the…
We investigate a tight binding quantum walk on a graph. Repeated stroboscopic measurements of the position of the particle yield a measured "trajectory", and a combination of classical and quantum mechanical properties for the walk are…
We calculate the large deviation function of the end-to-end distance and the corresponding extension-versus-force relation for (isotropic) random walks, on and off-lattice, with and without persistence, and in any spatial dimension. For…
We consider a random walker whose motion is tethered around a focal point. We use two models that exhibit the same spatial dependence in the steady state but widely different dynamics. In one case, the walker is subject to a deterministic…
We discuss the statistics of first-passage times of a Brownian particle moving in a highly unstable nonlinear potential proportional to an odd power of position. We observe temperature-induced shortening of the mean first-passage time and…
The dynamics of elongated inertial particles in an extensional flow is studied numerically by performing simulations of freely jointed bead-rod chains. The coil-stretch transition and the tumbling instability are characterized as a function…
Depending on how the dynamical activity of a particle in a random environment is influenced by an external field $E$, its differential mobility at intermediate $E$ can turn negative. We discuss the case where for slowly changing random…
We consider a discrete-time random walk on the nodes of an unbounded hexagonal lattice. We determine the probability generating functions, the transition probabilities and the relevant moments. The convergence of the stochastic process to a…
The cost of stochastic resetting is considered within the context of a discrete random walk model. In addition to standard stochastic resetting, for which a reset occurs with a certain probability after \emph{each} step, we introduce a…