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We study the collective motion of autonomous mobile agents on a ringlike environment. The agents' dynamics is inspired by known laboratory experiments on the dynamics of locust swarms. In these experiments, locusts placed at arbitrary…
We are interested in recovering information on a stochastic block model from the subgraph discovered by an exploring random walk. Stochastic block models correspond to populations structured into a finite number of types, where two…
Investigation of protein self-assembly processes is important for the understanding of the growth processes of functional proteins as well as disease-causing amyloids. Inside cells, intrinsic molecular fluctuations are so high that they…
This paper introduces a system of stochastic differential equations (SDE) of mean-field type that models pedestrian motion. The system lets the pedestrians spend time at, and move along, walls, by means of sticky boundaries and boundary…
We study random walks on Erd\"os-R\'enyi random graphs in which, every time the random walk returns to the starting point, first an edge probability is independently sampled according to a priori measure $\mu$, and then an Erd\"os-R\'enyi…
We discuss conditions for unique ergodicity of a collective random walk on a continuous circle. Individual particles in this collective motion perform independent (and different in general) random walks conditioned by the assumption that…
The goal of this paper is to provide mathematically rigorous tools for modelling the evolution of a community of interacting individuals. We model the population by a measure space where the measure determines the abundance of individual…
We address here the issue of congestion in the modeling of crowd motion, in the non-smooth framework: contacts between people are not anticipated and avoided, they actually occur, and they are explicitly taken into account in the model. We…
Scaling mobility patterns have been widely observed for animals. In this paper, we propose a deterministic walk model to understand the scaling mobility patterns, where walkers take the least-action walks on a lattice landscape and prey.…
There are various cases of animal movement where behaviour broadly switches between two modes of operation, corresponding to a long distance movement state and a resting or local movement state. Here a mathematical description of this…
Quantitatively modeling the trajectories and behavior of pedestrians walking in crowds is an outstanding fundamental challenge deeply connected with the physics of flowing active matter, from a scientific point of view, and having societal…
Many ant species employ distributed population density estimation in applications ranging from quorum sensing [Pra05], to task allocation [Gor99], to appraisal of enemy colony strength [Ada90]. It has been shown that ants estimate density…
We consider nearest neighbor weighted random walks on the $d$-dimensional box $[n]^d$ that are governed by some function $g:[0,1] \ra [0,\iy)$, by which we mean that standing at $x$, a neighbor $y$ of $x$ is picked at random and the walk…
Elephant random walk is a special type of random walk that incorporates the memory of the past to determine its future steps. The probability of this walk taking a particular step (+1 or -1) at a time point, conditioned on the entire…
We study a model for a random walk of two classes of particles (A and B). Where both species are present in the same site, the motion of A's takes precedence over that of B's. The model was originally proposed and analyzed in Maragakis et…
We analyze a variant of the Noisy $K$-Branching Random Walk, a population model that evolves according to the following procedure. At each time step, each individual produces a large number of offspring that inherit the fitness of their…
Place one active particle at the root of a graph and a Poisson-distributed number of dormant particles at the other vertices. Active particles perform simple random walk. Once the number of visits to a site reaches a random threshold, any…
The collective motion of groups of animals emerges from the net effect of the interactions between individual members of the group. In many cases, such as birds, fish, or ungulates, these interactions are mediated by sensory stimuli that…
Routing choices of walking pedestrians in geometrically complex environments are regulated by the interplay of a multitude of factors such as local crowding, (estimated) time to destination, (perceived) comfort. As individual choices…
Experimental studies of the diffusion of biomolecules in the environment of biological cells are routinely confronted with multiple sources of stochasticity, whose identification renders the detailed data analysis of single molecule…