Related papers: Mean trapping time for an arbitrary node on regula…
Understanding excitation and charge transfer in disordered media is a significant challenge in chemistry, biophysics and material science. We study two experimentally-relevant measures for carriers transfer in finite-size chains, the…
We study the first passage time (FPT) problem for biased continuous time random walks. Using the recently formulated framework of fractional Fokker-Planck equations, we obtain the Laplace transform of the FPT density function when the bias…
It has been recently reported that the reciprocity of real-life weighted networks is very pronounced, however its impact on dynamical processes is poorly understood. In this paper, we study random walks in a scale-free directed weighted…
A new mechanism for efficiently solving the Markov decision processes (MDPs) is proposed in this paper. We introduce the notion of reachability landscape where we use the Mean First Passage Time (MFPT) as a means to characterize the…
We study the mean time for a random walk to traverse between two arbitrary sites of the Erdos-Renyi random graph. We develop an effective medium approximation that predicts that the mean first-passage time between pairs of nodes, as well as…
First passage times (FPTs) are often used to study timescales in physical, chemical, and biological processes. FPTs generically describe the time it takes a random "searcher" to find a "target." In many systems, the important timescale is…
An efficient and accurate iterative scheme for the computation of the mean first passage times (MFPTs) of ergodic Markov chains has been presented. Firstly, the computation problem of MFPTs is transformed into a set of linear equations. It…
The study of first passage percolation (FPP) for the random interlacements model has been initiated in arXiv:2112.12096, where it is shown that on $\mathbb{Z}^d$, $d\geq 3$, the FPP distance is comparable to the graph distance with high…
The first passage is a generic concept for quantifying when a random quantity such as the position of a diffusing molecule or the value of a stock crosses a preset threshold (target) for the first time. The last decade saw an enlightening…
The purpose of this paper is to investigate several analytical methods of solving first passage (FP) problem for the Rouse model, a simplest model of a polymer chain. We show that this problem has to be treated as a multi-dimensional…
We revise the classical problem of characterizing first exit times of a harmonically trapped particle whose motion is described by one- or multi-dimensional Ornstein-Uhlenbeck process. We start by recalling the main derivation steps of a…
In this work we consider a class of recursively-grown fractal networks $G_n(t)$, whose topology is controlled by two integer parameters $t$ and $n$. We first analyse the structural properties of $G_n(t)$ (including fractal dimension,…
We theoretically study the trapping time distribution and the efficiency of the excitation energy transport in dendritic systems. Trapping of excitations, created at the periphery of the dendrimer, on a trap located at its core, is used as…
The first-passage time (FPT), i.e., the moment when a stochastic process reaches a given threshold value for the first time, is a fundamental mathematical concept with immediate applications. In particular, it quantifies the statistics of…
We study the statistical properties of the convex hull of a planar run-and-tumble particle (RTP), also known as the "persistent random walk", where the particle/walker runs ballistically between tumble events at which it changes its…
We present analytical results for the distribution of first hitting times of non-backtracking random walks on finite Erd\H{o}s-R\'enyi networks of $N$ nodes. The walkers hop randomly between adjacent nodes on the network, without stepping…
The trapping problem on graph (or network) as a typical focus of great interest has attracted more attention from various science fields, including applied mathematics and theoretical computer science, in the past. Here, we first study this…
The kinetics of a variety of transport-controlled processes can be reduced to the problem of determining the mean time needed to arrive at a given location for the first time, the so called mean first passage time (MFPT) problem. The…
We study the problem of a particle/message that travels as a biased random walk towards a target node in a network in the presence of traps. The bias is represented as the probability $p$ of the particle to travel along the shortest path to…
During a random search, resetting the searcher's position from time to time to the starting point often reduces the mean completion time of the process. Although many different resetting models have been studied over the past ten years,…