相关论文: The contact process seen from a typical infected s…
We provide finite-size scaling estimates for the dynamical critical exponent of the even parity-conserving universality class of critical behavior through exact numerical diagonalizations of the time evolution operator of an…
To every finitely generated group one can assign the conjugacy growth function that counts the number of conjugacy classes intersecting a ball of radius $n$. Results of Ivanov and Osin show that the conjugacy growth function may be constant…
In this paper we are concerned with contact processes on open clusters of oriented percolation in $Z^d$, where the disease spreads along the direction of open edges. We show that the two critical infection rates in the quenched and annealed…
We consider a general class of contact processes on $\mathbb{Z}^d$ with potentially long-range interactions. By adapting well established renormalization arguments to the long-range setting we extend by now classical results for…
For the supercritical contact process on the hyper-cubic lattice started from a single infection at the origin and conditioned on survival, we establish two uniformity results for the hitting times $t(x)$, defined for each site $x$ as the…
The regular tree corresponds to the random regular graph as its local limit. For this reason the famous double phase transition of the contact process on regular tree has been seen to correspond to a phase transition on the large random…
Disease, opinions, ideas, gossip, etc. all spread on social networks. How these networks are connected (the network structure) influences the dynamics of the spreading processes. By investigating these relationships one gains understanding…
We obtain exponential moment asymptotics for the Bessel point process. As a direct consequence, we improve on the asymptotics for the expectation and variance of the associated counting function, and establish several central limit…
The contact process is a stochastic process which exhibits a continuous, absorbing-state phase transition in the Directed Percolation (DP) universality class. In this work, we consider a contact process with a bias in conjunction with an…
We consider a generalization of the contact process stochastic model, including an additional autocatalitic process. The phase diagram of this model in the proper two-parameter space displays a line of transitions between an active and an…
Global strategies to contain a pandemic, such as social distancing and protective measures, are designed to reduce the overall transmission rate between individuals. Despite such measures, essential institutions, including hospitals,…
Contact tracing is one of the most important control measures deployed during epidemics. Relying on the identification of contacts of known infected individuals, it necessitates a network perspective. Although pairwise models have been used…
We study the effects of switching social contacts as a strategy to control epidemic outbreaks. Connections between susceptible and infective individuals can be broken by either individual, and then reconnected to a randomly chosen member of…
The extinction transition in the presence of a localized quenched defect is studied numerically. When the bulk is at criticality, the correlation length diverges and even an infinite system cannot "decouple" from the defect. The results…
We show results for the contact process on Barabasi networks. The contact process is a model for an epidemic spreading without permanent immunity that has an absorbing state. For finite lattices, the absorbing state is the true stationary…
A little over 25 years ago Pemantle pioneered the study of the contact process on trees, and showed that on homogeneous trees the critical values $\lambda_1$ and $\lambda_2$ for global and local survival were different. He also considered…
In this paper we will consider the contact process in a very simple type of random environment that physicists call the random dilution model. We start with the contact process on a graph, here either $\mathbb{Z}^d$, a $d$-dimensional torus…
It has been proposed (Phys. Rev. E {\bf 71}, 026121 (2005)) that unlike the short range contact process, a long-range counterpart may lead to the existence a discontinuous phase transition in one dimension. Aiming at exploring such link,…
The pair contact process (PCP) is a nonequilibrium stochastic model which, like the basic contact process (CP), exhibits a phase transition to an absorbing state. The two models belong to the directed percolation (DP) universality class,…
We study survival and extinction of a long-range infection process on a diluted one-dimensional lattice in discrete time. The infection can spread to distant vertices according to a Pareto distribution, however spreading is also prohibited…