Related papers: Sensitivity of the frog model to initial condition…

This paper studies a class of growing systems of random walks on regular trees, known as \emph{frog models with geometric lifetime} in the literature. With the help of results from renewal theory, we derive new bounds for their critical…

In this paper, we introduce a one-dimensional model of particles performing independent random walks, where only pairs of particles can produce offspring ("cooperative branching"), and particles that land on an occupied site merge with the…

Active particles under soft confinement such as droplets or vesicles present intriguing phenomena, as collective motion emerges alongside the deformation of the environment. A model is employed to systematically investigate droplet…

We present a model for a random walk with memory, phenomenologically inspired in a biological system. The walker has the capacity to remember the time of the last visit to each site and the step taken from there. This memory affects the…

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…

Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…

We consider an elementary model for self-organised criticality, the activated random walk on the complete graph. We introduce a discrete time Markov chain as follows. At each time step, we add an active particle at a random vertex and let…

This paper concerns the long-term behaviour of a system of interacting random walks labeled by vertices of a finite graph. The model is reversible which allows to use the method of electric networks in the study. In addition, examples of…

In this paper we consider a class of interacting particle systems on dynamic random networks, in which the joint dynamics of vertices and edges acts as one-way feedback, i.e., edges appear and disappear over time depending on the state of…

In this paper, we study a spatial model for dormancy in a random environment via a two-type branching random walk in continuous-time, where individuals switch between dormant and active states depending on the current state of a fluctuating…

Tracking of individual particle and studying their motion serves as a direct means to understand the dynamics in crowded and complex environments. In this study, the dynamics of tracer particles in the matrix of dense soft-colloidal…

Two classes of interacting particle systems on $\mathbb{Z}$ are shown to be Pfaffian point processes at fixed times, and for all deterministic initial conditions. The first comprises coalescing and branching random walks, the second…

A lattice model for active matter is studied numerically, showing that it displays wettings transitions between three distinctive phases when in contact with an impenetrable wall. The particles in the model move persistently, tumbling with…

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…

A quantitative model of the mobility of functionalized particles at the interface is pivotal to understanding important systems in biology and nanotechnology. In this work, we investigate the emerging dynamics of particles anchored through…

Abridged abstract: Inert interactions between randomly moving entities and spatial disorder play a crucial role in quantifying the diffusive properties of a system. These interactions affect only the movement of the entities, and examples…

Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…

A model of a device is proposed and related theoretical calculation is performed to study the weak interactions among neutral atoms and molecules. In this model 3-body collisions among the neutral particles occur repeatedly in a trap.…

We study memory based random walk models to understand diffusive motion in crowded heterogeneous environment. The models considered are non-Markovian as the current move of the random walk models is determined by randomly selecting a move…

Experiments on particles' motion in living cells show that it is often subdiffusive. This subdiffusion may be due to trapping, percolation-like structures, or viscoelatic behavior of the medium. While the models based on trapping (leading…