On the critical value function in the divide and color model

Mathematics – Probability

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Scientific paper

The divide and color model on a graph G arises by first deleting each edge of G with probability (1-p) independently of each other, then coloring the resulting connected components (i.e., every vertex in the component) black or white with respective probabilities r and (1-r), independently for different components. Viewing it as a (dependent) site percolation model, one can define the critical point r_c(p). In this paper, we first give upper and lower bounds for r_c(p) for general G via a stochastic comparison with Bernoulli percolation, and discuss (non-)monotonicity and (non-)continuity properties of r_c(p) in p. Then we focus on the case G=Z^2 and prove continuity of r_c(p) as a function of p in the interval [0,1/2), and we examine the asymptotic behavior of the critical value function as p tends to its critical value.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

On the critical value function in the divide and color model 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 On the critical value function in the divide and color model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the critical value function in the divide and color model will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-673683

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.