Asymptotic Properties of Random Subsets of Projective Spaces.
NORTH CAROLINA UNIV AT CHAPEL HILL INST OF STATISTICS
Pagination or Media Count:
A random graph on n vertices is a random subgraph of the complete graph on n vertices. By analogy with this, the present paper studies the asymptotic properties of a random submatroid omegar of the projective geometry PGr-1,q. The main result concerns Kr, the rank of the largest projective geometry occurring as a submatroid of omegar. We show that with probability one, for sufficiently large r, Kr takes one of at most two values depending on r. This theorem is analogous to a result of Bollobas and Erdos on the clique number of a random graph. However, whereas from the matroid theorem one can essentially determine the critical exponent of omegar, the graph theorem gives only a lower bound on the chromatic number of a random graph. Author
- Statistics and Probability