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Seminarium i matematik

Moments of a Class of Random Matrices

Välkommen till föreläsningen i seminarieserien i matematik.

Modern random matrix theory (RMT) traces its origins to the fields of
mathematics (through the works of Hurwitz) statistics (through Wishart) and
of high energy physics (Wigner). We will give a brief historical survey of
RMT and then proceed to the problem of deriving moments of functions of
certain random matrices. Of particular interest are Wishart matrices and
random matrices on the classical compact groups ( p) , ( p) and (2 p) . Some
of the standard machinery for deriving moments will be reviewed and some
open problems discussed, including the emergence of the Haar measure on
( ) p .
Keywords: Random matrices, moments, Weingarten calculus, Haar measure.