Random determinants
R. Fortet · Journal of research of the National Bureau of Standards · 1951
Determill a n ts whose cle ments involve random variables are disc ussed a nd expressions derived for t he first and second moments.Applica tio ns are made to n -dimens iona l geo me try , esp ecially , to findin g limi t in g p ro ba bili t ies for t he e ve nt: "a give n p oin t li es a bove a rand om hyp erplan e", under fairly general hy po t heses.The rando m variable AD h -B is co ns id ered , whe re An and B a re cer tain minors of t h e d eterminan tal equat ion of t he rand o m hy pe rplane, a nd h is a coordinate of t he given poin t . An asy mp toti c ex pression for E[A;! } is obtained, a nd it is shown t hat E[ 8 2 } is of t he ord er of (l I n) E [ A~}.