Exponential extinction time of the contact process on finite graphs

Details Exponential extinction time of the contact process on finite graphs Exponential extinction time of the contact process on finite graphs

2012-03-13

arxiv.org/abs/1203.2972v1

Mathematics

Probability

Scientific paper

We study the extinction time $\uptau$ of the contact process 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 $\uptau$ grows exponentially with the number of vertices. Additionally, for any sequence of growing trees of bounded degree, $\uptau$ divided by its expectation converges in distribution to the unitary exponential distribution. These also hold if one considers a sequence of graphs having spanning trees with uniformly bounded degree. Using these results, we consider the contact process on a random graph with vertex degrees following a power law. Improving a result of Chatterjee and Durrett \cite{CD}, we show that, for any infection rate, the extinction time for the contact process on this graph grows exponentially with the number of vertices.

Affiliated with

Also associated with

No associations

Rating

Exponential extinction time of the contact process on finite graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Exponential extinction time of the contact process on finite graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exponential extinction time of the contact process on finite graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-715042