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Probabilistic hyperdeterminantal inequalities

Presented by: 
A Gasparyan [PSI RAS]
Monday 23rd June 2008 - 16:20 to 17:00

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.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons