Related papers: Deviation bounds for the first passage time in the…
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 frog model with Bernoulli initial configuration, which is an interacting particle system on the multidimensional lattice consisting of two states of particles: active and sleeping. Active particles perform independent simple…
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…
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…
In this paper, we study the upper tail large deviation for the one-dimensional frog model. In this model, sleeping and active frogs are assigned to vertices on $\mathbb Z$. While sleeping frogs do not move, the active ones move as…
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 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…
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…
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…
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 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.…
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…
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…
We use a first-passage time approach to study the statistics of the trapping times induced by persistent motion of active particles colliding with flat boundaries. The angular first-passage time distribution and mean first-passage time is…
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 branching random walk on a graph in which particles branch only at unvisited sites. Consider an initial particle density of $\mu$ on the full $d$-ary tree of height $n$. If $\mu= \Omega( d^2)$, all of the vertices are…
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 a Poisson process on $\mathbb{R}$ with intensity $f$ where $0 \leq f(x)<\infty$ for ${x}\geq 0$ and ${f(x)}=0$ for $x<0$. The "points" of the process represent sleeping frogs. In addition, there is one active frog initially located…
The first passage time for a single diffusing particle has been studied extensively, but the first passage time of a system of many diffusing particles, as is often the case in physical systems, has received little attention until recently.…
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…