Related papers: On $L_1$-distance between first exit times from tw…
We present results for the ordered sequence of first passage times of arrival of N random walkers at a boundary in Euclidean spaces of d dimensions.
General upper bounds on fluctuations of trajectory observables were recently obtained. It turned out that the size of fluctuations of dynamical observable is limited from below and from above. For the moment generating function of general…
We consider processes that coincide with a given diffusion process outside a finite collection of domains. In each of the domains, there is, additionally, a large drift directed towards the interior of the domain. We describe the limiting…
In the scenario of the narrow escape problem (NEP) a particle diffuses in a finite container and eventually leaves it through a small "escape window" in the otherwise impermeable boundary, once it arrives to this window and over-passes an…
Time fractional advection-dispersion equations arise as generalizations of classical integer order advection-dispersion equations and are increasingly used to model fluid flow problems through porous media. In this paper we develop an…
We discuss the combined effects of overdamped motion in a quenched random potential and diffusion, in one dimension, in the limit where the diffusion coefficient is small. Our analysis considers the statistics of the mean first-passage time…
The timescales of many physical, chemical, and biological processes are determined by first passage times (FPTs) of diffusion. The overwhelming majority of FPT research studies the time it takes a single diffusive searcher to find a target.…
Subdiffusive motion of tracer particles in complex crowded environments, such as biological cells, has been shown to be widepsread. This deviation from brownian motion is usually characterized by a sublinear time dependence of the mean…
Despite having been studied for decades, first passage processes remain an active area of research. In this contribution we examine a particle diffusing in an annulus with an inner absorbing boundary and an outer reflective boundary. We…
We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain, for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion. The…
Local time is the measure of how much time a random walk has visited a given position. In multiple scattering media, where waves are diffuse, local time measures the sensitivity of the waves to the local medium's properties. Local…
The first-return time is the time that it takes a random walker to go back to the initial position for the first time. We study the first-return time when random walkers perform fractional kinetics, specifically fractional diffusion, that…
We show in detail some results, outlined in a previous paper regarding the case of Brownian motion (BM), about the distribution of the $n$th-passage time of a one-dimensional diffusion obtained by a space or time transformation of BM,…
We study the diffusion process in the presence of stochastic resetting inside a two-dimensional wedge of top angle $\alpha$, bounded by two infinite absorbing edges. In the absence of resetting, the second moment of the first-passage time…
A general criterion for the existence of phase separation in driven one-dimensional systems is proposed. It is suggested that phase separation is related to the size dependence of the steady-state currents of domains in the system. A…
We consider fast oscillating perturbations of dynamical systems in regions where one can introduce action-angle type coordinates. In an appropriate time scale, a diffusion approximation of the first-integrals evolution is described under…
The diffusion equation and its time-fractional counterpart can be obtained via the diffusion limit of continuous-time random walks with exponential and heavy-tailed waiting time distributions. The space dependent variable-order…
We investigate exceedances of the process over a sufficiently high threshold. The exceedances determine the risk of hazardous events like climate catastrophes, huge insurance claims, the loss and delay in telecommunication networks. Due to…
The escape of particles through a narrow absorbing gate in confined domains is a abundant phenomenon in various systems in physics, chemistry and molecular biophysics. We consider the narrow escape problem in a cellular flow when the two…
Rare events in the first-passage distributions of jump processes are capable of triggering anomalous reactions or series of events. Estimating their probability is particularly important when the jump probabilities have broad-tailed…