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Free convolution Michael Anshelevich
 

Summary: Free convolution
Michael Anshelevich
March 5, 2004
, probability measures on R. Their convolution
(S) =
R
(S - x) d(x).
Symmetrically,
R
f(z) d( )(z) =
RR
f(x + y) d(x) d(y).
Other definitions below.
EQUIVALENT DEFINITIONS OF FREE CONVOLUTION
1) Let 1, 2 be discrete groups (1 = 2 = Z works).
1 1 = their free product.
L(1), L(2), L(1 2) = group von Neumann alge-
bras.
All with distinguished (tracial) states.
1

  

Source: Anshelevich, Michael - Department of Mathematics, Texas A&M University

 

Collections: Mathematics