ON RANDOM DETERMINANTS I

Determillants whose clements involve random variables are discussed and expressions derived for the first and second moments. Applications are made to n-dimensional geometry, especially, to finding limiting probabilities for the event: "a given point lies above a random hyperplane", under fairly general hypotheses. The random variable ADh- B is considered, where An and B are certain minors of the determinantal equat ion of the random hyperplane, and h is a coordinate of the given point. An asymptotic expression for E[A;! } is obtained, and it is shown that E[ 8 2} is of t he order of (lIn) E [ A~}.