Perturbing the hexagonal circle packing: a percolation perspective

Details Perturbing the hexagonal circle packing: a percolation perspective Perturbing the hexagonal circle packing: a percolation perspective

2011-04-05

arxiv.org/abs/1104.0762v2

Mathematics

Probability

Fixed and extended proofs

Scientific paper

We consider the hexagonal circle packing with radius 1/2 and perturb it by letting the circles move as independent Brownian motions for time t. It is shown that, for large enough t, if \Pi_t is the point process given by the center of the circles at time t, then, as t\to\infty, the critical radius for circles centered at \Pi_t to contain an infinite component converges to that of continuum percolation (which was shown---based on a Monte Carlo estimate---by Balister, Bollob\'as and Walters to be strictly bigger than 1/2). On the other hand, for small enough t, we show (using a Monte Carlo estimate for a fixed but high dimensional integral) that the union of the circles contains an infinite connected component. We discuss some extensions and open problems.

Affiliated with

Also associated with

No associations

Rating

Perturbing the hexagonal circle packing: a percolation perspective 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 Perturbing the hexagonal circle packing: a percolation perspective, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Perturbing the hexagonal circle packing: a percolation perspective will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-320972