Related papers: A unifying approach to first-passage time distribu…
We introduce the concept of Randomly Modulated Gaussian Processes as a unifying framework for modeling, analyzing and classifying anomalous diffusion models in heterogeneous media. This formulation incorporates correlations in the…
The first-passage time is proposed as an independent thermodynamic parameter of the statistical distribution that generalizes the Gibbs distribution. The theory does not include the determination of the first passage statistics itself. A…
Quantifying how spatial disorder affects the movement of a diffusing particle or agent is fundamental to target search studies. When diffusion occurs on a network, that is on a highly disordered environment, we lack the mathematical tools…
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…
The transport of particles in cells is influenced by the properties of intracellular networks they traverse while searching for localized target regions or reaction partners. Moreover, given the rapid turnover in many intracellular…
We analyse the long-lasting effects of initial conditions on fluctuations in one-dimensional diffusive systems. We consider both the fluctuations of current for non-interacting diffusive particles starting from a step-like initial density…
We present rigorous results for the mean first passage time and first passage time statistics for two-channel Markov additive diffusion in a 3-dimensional spherical domain. Inspired by biophysical examples we assume that the particle can…
We present a study on the dynamics of a system consisting of a pair of hardcore particles diffusing with different rates. We solved the drift-diffusion equation for this model in the case when one particle, labeled F, drifts and diffuses…
We consider a bivariate diffusion process and we study the first passage time of one component through a boundary. We prove that its probability density is the unique solution of a new integral equation and we propose a numerical algorithm…
We study a reaction-diffusion process that involves two species of atoms, immobile and diffusing. We assume that initially only immobile atoms, uniformly distributed throughout the entire space, are present. Diffusing atoms are injected at…
We consider the drift and diffusion properties of periodically driven renewal processes. These processes are defined by a periodically time dependent waiting time distribution, which governs the interval between subsequent events. We show…
We explore the effect of stochastic resetting on the first-passage properties of space-dependent diffusion in presence of a constant bias. In our analytically tractable model system, a particle diffusing in a linear potential…
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…
We show that the distribution of times for a diffusing particle to first hit an absorber is \emph{independent} of the direction of an external flow field, when we condition on the event that the particle reaches the target for flow away…
Adsorption to a surface, reversible-binding, and trapping are all prevalent scenarios where particles exhibit "stickiness". Escape and first-passage times are known to be drastically affected, but detailed understanding of this phenomenon…
Biochemical processes in cells are governed by complex networks of many chemical species interacting stochastically in diverse ways and on different time scales. Constructing microscopically accurate models of such networks is often…
Motivated by recent single molecule studies of proteins sliding on a DNA molecule, we explore the targeting dynamics of N particles ("proteins") sliding diffusively along a line ("DNA") in search of their target site (specific target…
First passage under restart has recently emerged as a conceptual framework to study various stochastic processes under restart mechanism. Emanating from the canonical diffusion problem by Evans and Majumdar, restart has been shown to…
Consider a one dimensional diffusion process on the diffusion interval $I$ originated in $x_0\in I$. Let $a(t)$ and $b(t)$ be two continuous functions of $t$, $t>t_0$ with bounded derivatives and with $a(t)<b(t)$ and $a(t),b(t)\in I$,…
The aim of this paper is to analyze a class of random motions which models the motion of a particle on the real line with random velocity and subject to the action of the friction. The speed randomly changes when a Poissonian event occurs.…