Threshold distribution functions for some random representable matroids
JAMES G. OXLEY · Mathematical Proceedings of the Cambridge Philosophical Society · 1984
A random submatroid ωrof the projective geometryPG(r− 1,q) is obtained fromPG(r− 1,q) by deleting elements so that each element has, independently of all other elements, probability 1 −pof being deleted and probabilitypof being retained. The properties of such random structures were studied in [5] and [6]. In the first of these papers,pwas kept fixed, while in the second, motivated by Erdös and Rényi's work ([3), [4]) on random graphs,pwas taken to be a function ofr. A recent paper of Bollobás[2] strengthens and extends a number of the results of Erdös and Rényi. In this paper we prove matroid analogues of several of Bollobàs's results thereby extending some of the results of [6].