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We simulate a spatial behavioral model of the diffusion of an infection to understand the role of geographic characteristics: the number and distribution of outbreaks, population size, density, and agents' movements. We show that several…
For a graph $G$ on $n$ vertices, naively sampling the position of a random walk of at time $t$ requires work $\Omega(t)$. We desire local access algorithms supporting $\text{position}(G,s,t)$ queries, which return the position of a random…
Studying animal movements is essential for effective wildlife conservation and conflict mitigation. For aerial movements, operational weather radars have become an indispensable data source in this respect. However, partial measurements,…
We study the behavior of random walk on dynamical percolation. In this model, the edges of a graph G are either open or closed and refresh their status at rate \mu\ while at the same time a random walker moves on G at rate 1 but only along…
Random walks over directed graphs are used to model activities in many domains, such as social networks, influence propagation, and Bayesian graphical models. They are often used to compute the importance or centrality of individual nodes…
The statistics of first-passage times of random walks to target sites has proved to play a key role in determining the kinetics of space exploration in various contexts. In parallel, the number of distinct sites visited by a random walker…
In this work we study asymptotic properties of a long range memory random walk known as elephant random walk. First we prove recurrence and positive recurrence for the elephant random walk. Then, we establish the transience regime of the…
We study coupled transport in the nonequilibrium stationary state of a model consisting of independent random walkers, moving along a one-dimensional channel, which carry a conserved energy-like quantity, with density and temperature…
In animal societies as well as in human crowds, many observed collective behaviours result from self-organized processes based on local interactions among individuals. However, models of crowd dynamics are still lacking a systematic…
Collective animal movement fascinates children and scientists alike. One of the most commonly given explanations for collective animal movement is improved foraging. Animals are hypothesized to gain from searching for food in groups. Here,…
We consider a general discrete-time branching random walk on a countable set X. We relate local, strong local and global survival with suitable inequalities involving the first-moment matrix M of the process. In particular we prove that,…
The distribution of the first positive position reached by a random walker starting from the origin is fundamental for understanding the statistics of extremes and records in one-dimensional random walks. We present a comprehensive study of…
We investigate the dynamics of random walks on weighted networks. Assuming that the edge's weight and the node's strength are used as local information by a random walker, we study two kinds of walks, weight-dependent walk and…
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…
Consider a stochastic process that behaves as a $d$-dimensional simple and symmetric random walk, except that, with a certain fixed probability, at each step, it chooses instead to jump to a given site with probability proportional to the…
A correlated Gaussian random walk(CGRW) model is proposed as a simple model of animal dispersal. The general features of CGRW is described. We will discuss how from this single model a number of different kinds of correlated random walk can…
We present a prototype system that can be used to capture longitudinal socialising processes by recording people's encounters in space. We argue that such a system can usefully be deployed in prisons and other detention facilities in order…
We study a one-dimensional sluggish random walk with space-dependent transition probabilities between nearest-neighbour lattice sites. Motivated by trap models of slow dynamics, we consider a model in which the trap depth increases…
The spread of invasive species can have far reaching environmental and ecological consequences. Understanding invasion spread patterns and the underlying process driving invasions are key to predicting and managing invasions. We combine a…
The aim of this paper is to investigate the asymptotic behavior of the so-called elephant random walk with stops (ERWS). In contrast with the standard elephant random walk, the elephant is allowed to be lazy by staying on his own position.…