Related papers: Competing frogs on $\mathbb{Z}^d$
We study a system of random walks, known as the frog model, starting from a profile of independent Poisson($\lambda$) particles per site, with one additional active particle planted at some vertex $\mathbf{o}$ of a finite connected simple…
We consider the interacting particle system on the homogeneous tree of degree $(d + 1)$, known as frog model. In this model, active particles perform independent random walks, awakening all sleeping particles they encounter, and dying after…
Consider a growing system of random walks on the 3,2-alternating tree, where generations of nodes alternate between having two and three children. Any time a particle lands on a node which has not been visited previously, a new particle is…
We consider a slight modification of the frog model. For a given graph, each vertex has $\mathrm{Poisson}(\lambda)$ particles (or frogs). At time zero, only the particles at the origin are active, and all the other particles are sleeping.…
We study an interacting random walk system on Z where at time 0 there is an active particle at 0 and one inactive particle on each site $n \ge 1$. Particles become active when hit by another active particle. Once activated, the particle…
We study the frog model with death on the biregular tree $\mathbb{T}_{d_1,d_2}$. Initially, there is a random number of awake and sleeping particles located on the vertices of the tree. Each awake particle moves as a discrete-time…
Consider the following interacting particle system on the $d$-ary tree, known as the frog model: Initially, one particle is awake at the root and i.i.d. Poisson many particles are sleeping at every other vertex. Particles that are awake…
Consider a population of infinitesimally small frogs on the real line. Initially the frogs on the positive half-line are dormant while those on the negative half-line are awake and move according to the heat flow. At the interface, the…
We examine an interacting particle system on trees commonly referred to as the frog model. For its initial state, it begins with a single active particle at the root and i.i.d. $\mathrm{Poiss}(\lambda)$ many inactive particles at each…
The frog model is a system of random walks where active particles set sleeping particles in motion. On the complete graph with n vertices it is equivalent to a well-understood rumor spreading model. We given an alternate and elementary…
We consider a two-type stochastic competition model on the integer lattice Z^d. The model describes the space evolution of two ``species'' competing for territory along their boundaries. Each site of the space may contain only one…
The frog model is an infection process in which dormant particles begin moving and infecting others once they become infected. We show that on the rooted $d$-ary tree with particle density $\Omega(d^2)$, the set of visited sites contains a…
We introduce an extension of the frog model to Euclidean space and prove properties for the spread of active particles. Fix $r>0$ and place a particle at each point $x$ of a unit intensity Poisson point process $\mathcal P \subseteq \mathbb…
Place an active particle at the root of the infinite $d$-ary tree and dormant particles at each non-root site. Active particles move towards the root with probability $p$ and otherwise move to a uniformly sampled child vertex. When an…
This paper investigates the coexistence of two competing species on random geometric graphs (RGGs) in continuous time. The species grow by occupying vacant sites according to Richardson's model, while simultaneously competing for occupied…
We consider a random interacting particle system, known as the frog model, on infinite Galton-Watson trees allowing offspring zero and one. The system starts with one awake particle (frog) at the root of the tree and a random number of…
Random walkers characterized by random positions and random velocities lead to normal diffusion. A random walk was originally proposed by Einstein to model Brownian motion and to demonstrate the existence of atoms and molecules. Such a…
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…
Place an active particle at the root of a $d$-ary tree and a single dormant particle at each non-root site. In discrete time, active particles move towards the root with probability $p$ and, otherwise, away from the root to a uniformly…
We study a particle system with hopping (random walk) dynamics on the integer lattice $\mathbb Z^d$. The particles can exist in two states, active or inactive (sleeping); only the former can hop. The dynamics conserves the number of…