相关论文: Hitting and Trapping Times on Branched Structures

We derive an approximate formula for the mean first-passage time (MFPT) to a small absorbing target of arbitrary shape inside an elongated domain of a slowly varying axisymmetric profile. For this purpose, the original Poisson equation in…

We consider a system of asymmetric independent random walks on $\mathbb{Z}^d$, denoted by $\{\eta_t,t\in{\mathbb{R}}\}$, stationary under the product Poisson measure $\nu_{\rho}$ of marginal density $\rho>0$. We fix a pattern $\mathcal{A}$,…

Random walks constitute a fundamental mechanism for a large set of dynamics taking place on networks. In this article, we study random walks on weighted networks with an arbitrary degree distribution, where the weight of an edge between two…

The convergence, convergence rate and expected hitting time play fundamental roles in the analysis of randomised search heuristics. This paper presents a unified Markov chain approach to studying them. Using the approach, the sufficient and…

Continuous-time quantum walks have proven to be an extremely useful framework for the design of several quantum algorithms. Often, the running time of quantum algorithms in this framework is characterized by the quantum hitting time: the…

In this paper, we consider the problem of mean first-passage time (MFPT) in quantum mechanics; the MFPT is the average time of the transition from a given initial state, passing through some intermediate states, to a given final state for…

In the absence of acceleration, the velocity formula gives "distance travelled equals speed multiplied by time". For a broad class of Markov chains such as circulant Markov chains or random walk on complete graphs, we prove a probabilistic…

The hitting time is the required minimum time for a Markov chain-based walk (classical or quantum) to reach a target state in the state space. We investigate the effect of the perturbation on the hitting time of a quantum walk. We obtain an…

We describe an exact approach for calculating transition probabilities and waiting times in finite-state discrete-time Markov processes. All the states and the rules for transitions between them must be known in advance. We can then…

We use a first-passage time approach to study the statistics of the trapping times induced by persistent motion of active particles colliding with flat boundaries. The angular first-passage time distribution and mean first-passage time is…

We investigate the first-passage properties of nearest-neighbor hopping on a finite interval with disordered hopping rates. We develop an approach that relies on the backward equation, in conjunction with probability generating functions,…

We study the random walk problem on a deterministic scale-free network, in the presence of a set of static, identical targets; due to the strong inhomogeneity of the underlying structure the mean first-passage time (MFPT), meant as a…

Consider shuffling a deck of $n$ cards, labeled $1$ through $n$, as follows: at each time step, pick one card uniformly with your right hand and another card, independently and uniformly with your left hand; then swap the cards. How long…

We provide conditions that classify cover times for sequences of random walks on random graphs into two types: One type (Type 1) is the class of cover times that are of the order of the maximal hitting times scaled by the logarithm of the…

We study the mean traversal time for a class of random walks on Newman-Watts small-world networks, in which steps around the edge of the network occur with a transition rate F that is different from the rate f for steps across small-world…

We present analytical results for the distribution of cover times of random walks (RWs) on random regular graphs consisting of $N$ nodes of degree $c$ ($c \ge 3$). Starting from a random initial node at time $t=1$, at each time step $t \ge…

We demonstrate an implementation of the hitting time of a discrete time quantum random walk on cubelike graphs using IBM's Qiskit platform. Our implementation is based on efficient circuits for the Grover and Shift operators. We verify the…

A well-known theorem for an irreducible skip-free chain with absorbing state $d$, under some conditions, is that the hitting (absorbing) time of state $d$ starting from state 0 is distributed as the sum of $d$ independent geometric (or…

In this paper, we provide a methodology for computing the probability distribution of sojourn times for a wide class of Markov chains. Our methodology consists in writing out linear systems and matrix equations for generating functions…

Many known networks have structure of affiliation networks, where each of $n$ network's nodes (actors) selects an attribute set from a given collection of $m$ attributes and two nodes (actors) establish adjacency relation whenever they…