Related papers: Stroboscopic observation of a random walker
The analysis of contagion-diffusion processes in metapopulations is a powerful theoretical tool to study how mobility influences the spread of communicable diseases. Nevertheless, many metapopulation approaches use indistinguishable agents…
We analyze a one-dimensional intermittent random walk on an unbounded domain in the presence of stochastic resetting. In this process, the walker alternates between local intensive search, diffusion, and rapid ballistic relocations in which…
We study the dynamics of information (or virus) dissemination by $m$ mobile agents performing independent random walks on an $n$-node grid. We formulate our results in terms of two scenarios: broadcasting and gossiping. In the broadcasting…
We investigate crossing path probabilities for two agents that move randomly in a bounded region of the plane or on a sphere (denoted $R$). At each discrete time-step the agents move, independently, fixed distances $d_1$ and $d_2$ at angles…
Recent research highlighted the scaling property of human and animal mobility. An interesting issue is that the exponents of scaling law for animals and humans in different situations are quite different. This paper proposes a general…
Finding efficient algorithms to explore large networks with the aim of recovering information about their structure is an open problem. Here, we investigate this challenge by proposing a model in which random walkers with previously…
In this paper, we consider a stochastic process that may experience random reset events which relocate the system to its starting position. We focus our attention on a one-dimensional, monotonic continuous-time random walk with a constant…
Stochastic models of diffusion are routinely used to study dispersal of populations, including populations of animals, plants, seeds and cells. Advances in imaging and field measurement technologies mean that data are often collected across…
In applications like environment monitoring and pollution control, physical quantities are modeled by spatio-temporal fields. It is of interest to learn the statistical distribution of such fields as a function of space, time or both. In…
Combs are a simple caricature of various types of natural branched structures, which belong to the category of loopless graphs and consist of a backbone and branches. We study continuous time random walks on combs and present a generic…
This article investigates the pedestrian group as an emergent agent. The article explores empirical data to derive emergent agency and formation state spaces and outline recurring patterns of walking behavior. In this analysis, pedestrian…
We consider a one-dimensional infinite lattice where at each site there sits an agent carrying a velocity, which is drawn initially for each agent independently from a common distribution. This system evolves as a Markov process where a…
Focusing on a continuous-time quantum walk on $\mathbb{Z}=\left\{0,\pm 1,\pm 2,\ldots\right\}$, we analyze a probability distribution with which the quantum walker is observed at a position. The walker launches off at a localized state and…
Given a connected region in two-dimensional space where events of a certain kind occur according to a certain time-varying density, we consider the problem of setting up a network of autonomous mobile agents to detect the occurrence of…
In this paper we consider a telegraph equation with time-dependent coefficients, governing the persistent random walk of a particle moving on the line with a time-varying velocity $c(t)$ and changing direction at instants distributed…
With the popularity of portable wireless devices it is important to model and predict how information or contagions spread by natural human mobility -- for understanding the spreading of deadly infectious diseases and for improving delay…
The statistics of records for a time series generated by a continuous time random walk is studied, and found to be independent of the details of the jump length distribution, as long as the latter is continuous and symmetric. However, the…
We consider continuous-time random walk models described by arbitrary sojourn time probability density functions. We find a general expression for the distribution of time-averaged observables for such systems, generalizing some recent…
There have been extensive studies of a random walk among a field of immobile traps (or obstacles), where one is interested in the probability of survival as well as the law of the random walk conditioned on its survival up to time $t$. In…
In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly…