Yoshiaki Itoh, P. L. Krapivsky
We study a class of infinite directed random graphs. In these graphs, the interval [0,x] is the vertex set, while links are generated at random according to the following procedure: From each point y in the interval [0,x], directed links are drawn to points y' in the interval (y,x] which are chosen uniformly with density one. We analyze the length of the longest directed path starting from the origin. In the large x limit, we employ traveling wave techniques to extract the asymptotic behavior of this quantity. We also study the size of a cascade tree composed of vertices which can be reached via directed paths starting at the origin.
View original:
http://arxiv.org/abs/1206.3711
No comments:
Post a Comment