Related papers: Explicit determination of mean first-passage time …
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…
We derive a general exact formula for the mean first passage time (MFPT) from a fixed point inside a planar domain to an escape region on its boundary. The underlying mixed Dirichlet-Neumann boundary value problem is conformally mapped onto…
As a model of trapping by biased motion in random structure, we study the time taken for a biased random walk to return to the root of a subcritical Galton-Watson tree. We do so for trees in which these biases are randomly chosen,…
We investigate the average hitting times of simple random walks on the $k$-th power graph $C_N^k$ of the cycle graph $C_N$. First, we show that the average hitting times are characterized by a difference equation corresponding to the graph…
We analyze the diffusion of charged and neutral tracers suspended in an electrolyte embedded in a channel of varying cross-section. Making use of systematic approximations, the diffusion equation governing the motion of tracers is mapped…
Understanding the topological characteristics of complex networks and how they affect navigability is one of the most important goals in science today, as it plays a central role in various economic, biological, ecological and social…
Random walks, and in particular, their first passage times, are ubiquitous in nature. Using direct enumeration of paths, we find the first return time distribution of a 1D random walker, which is a heavy-tailed distribution with infinite…
We study one-dimensional discrete as well as continuous time random walks, either with a fixed number of steps (for discrete time) $n$ or on a fixed time interval $T$ (for continuous time). In both cases, we focus on symmetric probability…
For many stochastic dynamic systems, the Mean First Passage Time (MFPT) is a useful concept, which gives expected time before a state of interest. This work is an extension of MFPT in several ways. (1) We show that for some systems the…
The first passage time (FPT) is a generic measure that quantifies when a random quantity reaches a specific state. We consider the FTP distribution in nonlinear stochastic biochemical networks, where obtaining exact solutions of the…
We study a one-dimensional run-and-tumble particle (RTP), which is a prototypical model for active system, moving within an arbitrary external potential. Using backward Fokker-Planck equations, we derive the differential equation satisfied…
We study a generalisation of the random recursive tree (RRT) model and its multigraph counterpart, the uniform directed acyclic graph (DAG). Here, vertices are equipped with a random vertex-weight representing initial inhomogeneities in the…
We present analytical results for the joint probability distribution $P(T_{FR}=t,S=s)$ of first return (FR) times t and of the number of distinct sites s visited by a random walk (RW) on a one dimensional lattice before returning to the…
Self-interacting random walks are endowed with long range memory effects that emerge from the interaction of the random walker at time $t$ with the territory that it has visited at earlier times $t'<t$. This class of non Markovian random…
The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…
We consider random walks in which the walk originates in one set of nodes and then continues until it reaches one or more nodes in a target set. The time required for the walk to reach the target set is of interest in understanding the…
We study the asymptotic behavior of ``true" self-avoiding random walks on general infinite locally finite trees. In this model, the walk starts at the root and, at each step, from its current vertex chooses a neighboring edge to traverse…
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…
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…
We develop a high order asymptotic expansion for the mean first passage time (MFPT) of the capture of Brownian particles by a small elliptical trap in a bounded two dimensional region. This new result describes the effect that trap…