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We consider the Activated Random Walk model in any dimension with any sleep rate and jump distribution and ergodic initial state. We show that the stabilization properties depend only on the average density of particles, regardless of how…
Systems of active particles can show a large variety of collective behavior. In theory, two aspects determine the collective behavior: the model at the particle level and the parameter regime. While many studies consider a single model and…
Many collective systems exist in nature far from equilibrium, ranging from cellular sheets up to flocks of birds. These systems reflect a form of active matter, whereby individual material components have internal energy. Under specific…
In this work, we study the dynamics of a single active Brownian particle, as well as the collective behavior of interacting active Brownian particles, in a fluctuating heterogeneous environment. We employ a variant of the diffusing…
Spreading processes on top of active dynamics provide a novel theoretical framework for capturing emerging collective behavior in living systems. I consider run-and-tumble dynamics coupled with coagulation/decoagulation reactions that lead…
We study active run-and-tumble particles with an additional two-state internal variable characterizing their motile or non-motile state. Motile particles change irreversibly into non-motile ones upon collision with a non-motile particle.…
We consider the following interacting particle system: There is a ``gas'' of particles, each of which performs a continuous-time simple random walk on $\mathbb{Z}^d$, with jump rate $D_A$. These particles are called $A$-particles and move…
Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including…
Thanks to recent technological advances, it is now possible to track with an unprecedented precision and for long periods of time the movement patterns of many living organisms in their habitat. The increasing amount of data available on…
We study absorbing phase transitions in the one-dimensional branching annihilating random walk with long-range repulsion. The repulsion is implemented as hopping bias in such a way that a particle is more likely to hop away from its closest…
We consider a system of independent branching random walks on $\R$ which start off a Poisson point process with intensity of the form $e_{\lambda}(du)=e^{-\lambda u}du$, where $\lambda\in\R$ is chosen in such a way that the overall…
We introduce a simple model of active transport for an ensemble of particles driven by an external shear flow. Active refers to the fact that the flow of the particles is modified by the distribution of particles itself. The model consists…
Bootstrap percolation is a prominent framework for studying the spreading of activity on a graph. We begin with an initial set of active vertices. The process then proceeds in rounds, and further vertices become active as soon as they have…
We study asymptotic properties of the system of interacting diffusion particles on the real line which transfer a mass [arXiv:1408.0628]. The system is a natural generalization of the coalescing Brownian motions. The main difference is that…
The relaxation dynamics of zero range process (ZRP) has always been an interesting problem. In this study, we set up the relationship between ZRP and traps model, and investigate the slow dynamics of ZRP in the framework of traps model.…
Flow through passive porous media is typically described in terms of a linear theory relating current fluxes and driving forces, in the presence of a prescribed heterogeneous permeability. However, many porous systems such as glacial…
Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…
A class of interacting particle systems on $\mathbb{Z}$, involving instantaneously annihilating or coalescing nearest neighbour random walks, are shown to be Pfaffan point processes for all deterministic initial conditions. As diffusion…
Contagion processes, representing the spread of infectious diseases, information, or social behaviors, are often schematized as taking place on networks, which encode for instance the interactions between individuals. The impact of the…
Most spreading processes require spatial proximity between agents. The stationary state of spreading dynamics in a population of mobile agents thus depends on the interplay between the time and length scales involved in the epidemic process…