Related papers: Lipschitz-type estimate for the frog model with Be…
The frog model with a Bernoulli initial configuration is an interacting particle system on the $d$-dimensional lattice ($d \geq 2$) with two types of particles: active and sleeping. Active particles perform independent simple random walks.…
We consider the so-called frog model with random initial configurations. The dynamics of this model is described as follows: Some particles are randomly assigned on any site of the multidimensional cubic lattice. Initially, only particles…
The frog model is an interacting particle system on a graph. Active particles perform independent simple random walks, while sleeping particles remain inert until visited by an active particle. Some number of sleeping particles are placed…
Consider a stochastic growth model on $\mathbb{Z} ^d$. Start with some active particle at the origin and sleeping particles elsewhere. The initial number of particles at $x \in \mathbb{Z} ^d$ is $\eta(x)$, where $\eta (x)$ are independent…
The frog model is a stochastic model for the spreading of an epidemic on a graph, in which a dormant particle starts to perform a simple random walk on the graph and to awake other particles, once it becomes active. We study two versions of…
A two-type version of the frog model on $\mathbb{Z}^d$ is formulated, where active type $i$ particles move according to lazy random walks with probability $p_i$ of jumping in each time step ($i=1,2$). Each site is independently assigned a…
We study a system of simple random walks on graphs, known as frog model. This model can be described as follows: There are active and sleeping particles living on some graph G. Each active particle performs a simple random walk with…
The frog model starts with one active particle at the root of a graph and some number of dormant particles at all nonroot vertices. Active particles follow independent random paths, waking all inactive particles they encounter. We prove…
We study the frog model on \( \mathbb{Z} \) with geometric lifetimes, introducing a random survival parameter. Active and inactive particles are placed at the vertices of \( \mathbb{Z} \). The lifetime of each active particle follows a…
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 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 prove a shape theorem for a growing set of simple random walks on Z^d, known as frog model. The dynamics of this process is described as follows: There are active particles, which perform independent discrete time SRWs, and sleeping…
In this paper, we introduce a spatial model for dormancy in random environment via a two-type branching random walk in continuous-time, where individuals can switch between dormant and active states through spontaneous switching independent…
We consider an interacting particle system on trees known as the frog model: initially, a single active particle begins at the root and i.i.d.~$\mathrm{Poiss}(\lambda)$ many inactive particles are placed at each non-root vertex. Active…
We examine a system of interacting random walks with leftward drift on $\mathbb{Z}$, which begins with a single active particle at the origin and some distribution of inactive particles on the positive integers. Inactive particles become…
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…
The frog model is a system of interacting random walks. Initially, there is one particle at each vertex of a connected graph $\mathcal{G}$. All particles are inactive at time zero, except for the one which is placed at the root of…
We study the dynamics of a particle moving in one-dimensional Lorentz lattice-gas where particle performs mainly three different kinds of motion {\it viz} ballistic motion, diffusion and confinement. There are two different types of…
We consider the standard model of i.i.d. first passage percolation on $\mathbb{Z}^d$ given a distribution $G$ on $[0,+\infty]$ ($+\infty$ is allowed). When $G([0,+\infty]) < p_c(d)$, it is known that the time constant $\mu_G$ exists. We are…