Continuum Cascade Model of Directed Random Graphs: Traveling Wave Analysis
Probability
2012-10-31 v2 Statistical Mechanics
Populations and Evolution
Abstract
We study a class of directed random graphs. In these graphs, the interval [0,x] is the vertex set, and from each y\in [0,x], directed links are drawn to points 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.
Cite
@article{arxiv.1206.3711,
title = {Continuum Cascade Model of Directed Random Graphs: Traveling Wave Analysis},
author = {Yoshiaki Itoh and P. L. Krapivsky},
journal= {arXiv preprint arXiv:1206.3711},
year = {2012}
}
Comments
12 pages, 2 figures; figure added