Exponential extinction time of the contact process on finite graphs
By Thomas Mountford, Jean-Christophe Mourrat, Daniel Valesin, Qiang Yao. 2012
65 citations recorded by the source corpus.
We study the extinction time τ of the contact process started with full occupancy on finite trees of bounded degree. We show that, if the infection rate is larger than the critical rate for the contact process on Z, then, uniformly over all trees of degree bounded by a given number, the expectation of τ grows exponentially with the number of vertices. Additionally, for any increasing sequence of trees of bounded degree, τ divided by its expectation converges in distribution to the unitary exponential distribution. These results also hold if one considers a sequence of graphs having spanning trees with uniformly bounded degree, and provide the basis for powerful coarse-graining arguments. To demonstrate this, we consider the contact process on a random graph with vertex degrees following a power law. Improving a result of Chatterjee and Durrett (2009), we show that, for any non-zero infection rate, the extinction time for the contact process on this graph grows exponentially with the number of vertices.
Subfields: Mathematical Physics, Statistical and Nonlinear Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/fdb37e3f24dcc86bef1775193558a1a561bf8f50
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Mathematical Physics
In Statistical and Nonlinear Physics
In Statistics and Probability
Citations in the corpus
- Metastable densities for the contact process on power law random graphs (2013, background): “In [12], the result of [2] was improved and the extinction time was shown to grow as an exponential function of n.”
- Analysis and Control of Epidemics: A Survey of Spreading Processes on Complex Networks (2015, background): “The works [43], [64], and [65] show that there exists some critical value c x of the infection strength for which the expected time to extinction grows exponentially with N when .”