相关论文: Convergence rates for subcritical threshold-one co…
We present a method of general applicability for finding exact or accurate approximations to bond percolation thresholds for a wide class of lattices. To every lattice we sytematically associate a polynomial, the root of which in $[0,1]$ is…
We study the contact process with stirring on $\mathbb{Z}^d$. In this process, particles occupy vertices of $\mathbb{Z}^d$; each particle dies with rate 1 and generates a new particle at a randomly chosen neighboring vertex with rate…
We study the following bootstrap percolation process: given a connected graph $G$, a constant $\rho \in [0, 1]$ and an initial set $A \subseteq V(G)$ of \emph{infected} vertices, at each step a vertex~$v$ becomes infected if at least a…
We study the contact process on a random bipartite connection hypergraph generated from two Poisson point processes, with mark-dependent connection thresholds. For asymmetric infection rates and asymmetric power law tail decays of the two…
The contact process on dynamic edges (CPDE) is a contact process evolving on a dynamic environment given by a dynamical percolation on the edges of Z d\,: each edge updates its state to open or closed with respective rates vp and v(1 -p).…
We consider the cardinality of supercritical oriented bond percolation in two dimensions. We show that, whenever the origin is conditioned to percolate, the process appropriately normalized converges asymptotically in distribution to the…
We consider first-passage percolation on the $d$ dimensional cubic lattice for $d \geq 2$; that is, we assign independently to each edge $e$ a nonnegative random weight $t_e$ with a common distribution and consider the induced random graph…
In this paper, we establish the necessary and sufficient criterion for the contact process on Galton-Watson trees (resp. random graphs) to exhibit the phase of extinction (resp. short survival). We prove that the survival threshold…
We propose an approach to approximate the boundary crossing probabilities for general one-dimensional diffusion processes, and derive the convergence rate for this approximation scheme. There results are based on the explicit expression of…
We study limit laws for simple random walks on supercritical long-range percolation clusters on the integer lattice. For the long range percolation model, the probability that two vertices are connected behaves asymptotically as a negative…
We study a contact process running in a random environment in $\mathbb {Z}^d$ where sites flip, independently of each other, between blocking and nonblocking states, and the contact process is restricted to live in the space given by…
We consider random graphs with uniformly bounded edges on a Poisson point process conditioned to contain the origin. In particular we focus on the random connection model, the Boolean model and Miller-Abrahams random resistor network with…
We study the limiting behavior of an interacting particle system evolving on the lattice $Z^{d}$ for $d\ge 3$. The model is known as the contact process with rapid stirring. The process starts with a single particle at the origin. Each…
We study the asymptotic behaviour of the survival probability of a multi-type branching processes in random environment. The class of processes we consider corresponds, in the one-dimensional situation, to the intermediately subcritical…
In this paper, we consider the threshold-one contact process and the threshold-one voter model w/o spontaneous death on homogeneous trees $\mathbb{T}_d$, $d\ge 2$. Mainly inspired by the corresponding arguments for ordinary contact…
We study the growth of two competing infection types on graphs generated by the configuration model with a given degree sequence. Starting from two vertices chosen uniformly at random, the infection types spread via the edges in the graph…
The contact process is a particular case of birth-and-death processes on infinite particle configurations. We consider the contact models on locally compact separable metric spaces. We prove the existence of a one-parameter set of invariant…
We study atypical behavior in bootstrap percolation on the Erd\H{o}s-R\'enyi random graph. Initially a set $S$ is infected. Other vertices are infected once at least $r$ of their neighbors become infected. Janson et al. (2012) locates the…
We consider an isolated point defect embedded in a homogeneous crystalline solid. We show that, in the harmonic approximation, a periodic supercell approximation of the formation free energy as well as of the transition rate between two…
We investigate bootstrap percolation with infection threshold $r> 1$ on the binomial $k$-uniform random hypergraph $H_k(n,p)$ in the regime $n^{-1}\ll n^{k-2}p \ll n^{-1/r}$, when the initial set of infected vertices is chosen uniformly at…