相关论文: Random spreading phenomena in annealed small world…

We investigate the number $V_p(n)$ of distinct sites visited by an $n$-step resetting random walker on a $d$-dimensional hypercubic lattice with resetting probability $p$. In the case $p=0$, we recover the well-known result that the average…

We study the long-time behavior of the probability density associated with the decoupled continuous-time random walk which is characterized by a superheavy-tailed distribution of waiting times. It is shown that if the random walk is…

Consider the following routing problem in the context of a large scale network $G$, with particular interest paid to power law networks, although our results do not assume a particular degree distribution. A small number of nodes want to…

We investigate searching efficiency of different kinds of random walk on complex networks which rely on local information and one-step memory. For the studied navigation strategies we obtained theoretical and numerical values for the graph…

We analyse the so-called small-world network model (originally devised by Strogatz and Watts), treating it, among other things, as a case study of non-linear coupled difference or differential equations. We derive a system of evolution…

We consider wetting of a one-dimensional random walk on a half-line $x\ge 0$ in a short-ranged potential located at the origin $x=0$. We demonstrate explicitly how the presence of a quenched chemical disorder affects the pinning-depinning…

We introduce a non-equilibrium discrete-time random walk model on multiplex networks, in which at each time step the walker first undergoes a random jump between neighboring nodes in the same layer, and then tries to hop from one node to…

We analyze the dynamics of the Sisyphus random walk model, a discrete Markov chain in which the walkers may randomly return to their initial position $x_0$. In particular, we present a remarkably compact derivation of the time-dependent…

Random walks are a fundamental tool for analyzing realistic complex networked systems and implementing randomized algorithms to solve diverse problems such as searching and sampling. For many real applications, their actual effect and…

Random walk is one of the basic mechanisms found in many network applications. We study the epidemic spreading dynamics driven by biased random walks on complex networks. In our epidemic model, each time infected nodes constantly spread…

The probability distribution of the number $s$ of distinct sites visited up to time $t$ by a random walk on the fully-connected lattice with $N$ sites is first obtained by solving the eigenvalue problem associated with the discrete master…

We analyze a special class of 1-D quantum walks (QWs) realized using optical multi-ports. We assume non-perfect multi-ports showing errors in the connectivity, i.e. with a small probability the multi- ports can connect not to their nearest…

We obtain the exact asymptotic result for the disorder-averaged probability distribution function for a random walk in a biased Sinai model and show that it is characterized by a creeping behavior of the displacement moments with time,…

We consider discrete-time nearest-neighbor quantum walks on random environments in one dimension. Using the method based on a path counting, we present both quenched and annealed weak limit theorems for the quantum walk.

Recently, random walks on dynamic graphs have been studied because of their adaptivity to the time-varying structure of real-world networks. In general, there is a tremendous gap between static and dynamic graph settings for the lazy simple…

Efficient techniques to navigate networks with local information are fundamental to sample large-scale online social systems and to retrieve resources in peer-to-peer systems. Biased random walks, i.e. walks whose motion is biased on…

In this paper, we use a series of small world networks to simulate the epidemic spreading in the real world. To make our model more similar to the real world, we employ a parameter $p_{move}$ to denote its moving probability, which…

We study the relaxation time in the random walk with jumps. The random walk with jumps combines random walk based sampling with uniform node sampling and improves the performance of network analysis and learning tasks. We derive various…

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…

The usual development of the continuous-time random walk (CTRW) proceeds by assuming that the present is one of the jumping times. Under this restrictive assumption integral equations for the propagator and mean escape times have been…