Stan Szarek
Case Western Reserve University
Concentration for
non-commutative polynomials
in Wigner ensembles
The last dozen or so years dramatically improved our understanding
of concentration of various functionals of random matrices. Still, a
number
of unresolved questions remains. One difficult issue is generalizing
facts which are known for Gaussian matrices to general subgaussian
ensembles or to Wigner ensembles. We sketch an argument, in the spirit of
Talagrand-Guionnet-Zeitouni, showing exponential concentration for
the trace of (non-commutative) polynomials in Wigner-type random matrices.