most recent 30 from http://mathoverflow.net 2013-05-25T22:38:12Z http://mathoverflow.net/feeds/question/88503 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/88503/the-mean-number-of-vertices-in-small-connected-components-of-random-geometric-gra EclipseInterlude 2012-02-15T09:30:14Z 2012-02-15T16:12:32Z

<p>I place $N$ points on a circular plane of radius $R$, and draw edges to connect points that are less than or equal to some distance $D$ to form a set of graphs or cliques $G_i$. As a function of $N$, $R$, and $D$, what is the mean number of points, $m_k$, that participate in graphs with $k$ or fewer vertices?</p> <p>To clarify, the $N$ points are randomly placed on the circular plane with uniform probability across its surface.</p>