Related papers: Metastable behavior for bootstrap percolation on r…
We consider the discrete-time threshold-$\theta \ge 2$ contact process on a random r-regular graph on n vertices. In this process, a vertex with at least \theta occupied neighbors at time t will be occupied at time t+1 with probability p,…
Bootstrap percolation on the random graph $G_{n,p}$ is a process of spread of "activation" on a given realization of the graph with a given number of initially active nodes. At each step those vertices which have not been active but have at…
On the rooted $k$-ary tree we consider a 0-1 kinetically constrained spin model in which the occupancy variable at each node is re-sampled with rate one from the Bernoulli(p) measure iff all its children are empty. For this process the…
In this paper we study the properties of the Barab\'asi model of queueing under the hypothesis that the number of tasks is steadily growing in time. We map this model exactly onto an Invasion Percolation dynamics on a Cayley tree. This…
A bootstrap percolation process on a graph $G$ is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least $r$ infected neighbours…
Bootstrap percolation is a wide class of monotone cellular automata with random initial state. In this work we develop tools for studying in full generality one of the three `universality' classes of bootstrap percolation models in two…
We study bootstrap percolation (BP) on hyperbolic lattices obtained by regular tilings of the hyperbolic plane. Our work is motivated by the connection between the BP transition and the dynamical transition of kinetically constrained…
Let $G_{n,p}^1$ be a superposition of the random graph $G_{n,p}$ and a one-dimensional lattice: the $n$ vertices are set to be on a ring with fixed edges between the consecutive vertices, and with random independent edges given with…
Two-dimensional bootstrap percolation is usually characterized by bulk observables, but whether increasing the activation threshold qualitatively reorganizes the geometry of the absorbing state has remained unclear. Here we show that the…
We consider Bernoulli bond percolation on oriented regular trees, where besides the usual short bonds, all bonds of a certain length are added. Independently, short bonds are open with probability $p$ and long bonds are open with…
In majority bootstrap percolation on a graph G, an infection spreads according to the following deterministic rule: if at least half of the neighbours of a vertex v are already infected, then v is also infected, and infected vertices remain…
We study the $m=3$ bootstrap percolation model on a cubic lattice, using Monte Carlo simulation and finite-size scaling techniques. In bootstrap percolation, sites on a lattice are considered occupied (present) or vacant (absent) with…
Majority bootstrap percolation on the random graph $G_{n,p}$ is a process of spread of "activation" on a given realisation of the graph with a given number of initially active nodes. At each step those vertices which have more active…
We consider bootstrap percolation on uncorrelated complex networks. We obtain the phase diagram for this process with respect to two parameters: $f$, the fraction of vertices initially activated, and $p$, the fraction of undamaged vertices…
We introduce and study two variants of two-stage growth dynamics in $\mathbb{Z}^2$ with state space $\{0,1,2\}^{\mathbb{Z}^2}$. In each variant, vertices in state $0$ can be changed irreversibly to state $1$, and vertices in state $1$ can…
We introduce and study a new percolation model, inspired by recent works on jigsaw percolation, graph bootstrap percolation, and percolation in polluted environments. Start with an oriented graph $G_0$ of initially occupied edges on $n$…
We study qualitative properties of two-dimensional freezing cellular automata with a binary state set initialized on a random configuration. If the automaton is also monotone, the setting is equivalent to bootstrap percolation. We explore…
We numerically study bootstrap percolation on Kleinberg's spatial networks, in which the probability density function of a node to have a long-range link at distance $r$ scales as $P(r)\sim r^{\alpha}$. Setting the ratio of the size of the…
Random walks and diffusions in symmetric random environment are known to exhibit metastable behavior: they tend to stay for long times in wells of the environment. For the case that the environment is a one-dimensional two-sided standard…
In graph bootstrap percolation, edges of an Erd\H{o}s-R\'enyi random graph ${\mathcal G}_{n,p}$ are initially active. Activation spreads to other edges of the complete graph $K_n$ by an iterative process governed by a fixed graph $H$,…