Probabilistic hyperdeterminantal inequalities
Babbage, Pembroke St.
Over many years I was interested in possible foundation of a multidimensional matrix theory involving multidimensional determinants and other tensor generalizations of usual matrix structures. As a result one can notify series of hyperdeterminantal identities from which I derive probabilistic inequalities concerning n-ary scalar products, means, correlations and higher moments of random variables. This makes possible generalization of many classical and recent results on Greene functions, Bogoliubov quasimeans, cummulants and some other quantities. Among results we indicate several generalizations of Chebyshev, Griffiths and other FKG-type inequalities.