Department of Mathematics

Mathematical Physics and Operator Algebras

  •  Brent Nelson, Vanderbilt and MSU
  •  Free Stein Information
  •  03/19/2019
  •  11:00 AM - 12:00 PM
  •  C304 Wells Hall

Given a von Neumann algebra M equipped with a trace, any self-adjoint operator in M can be thought of as a non-commutative random variable. For an n-tuple X of such operators, the free Stein information of X is a free probabilistic quantity defined by the behavior of a non-commutative Jacobian on the polynomial algebra generated by entries of X. It is a number in the interval [0,n] and its value can provide information about the entries of X as well as the von Neumann algebra they generate. In this talk, I will discuss these and other properties of the free Stein information and consider a few examples where it can be explicitly computed. This is based on joint work with Ian Charlesworth.



Department of Mathematics
Michigan State University
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C212 Wells Hall
East Lansing, MI 48824

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