Summary: Free Processes via Matrix Theory
Concentration week on free Probability
Texas A&M, July 9-13.
Paris VI University
July 10, 2007
Nizar Demni Paris VI University Free Processes via Matrix Theory Concentration week on free Pr
Non commutative probability space :
Unital Algebra A + linear functional : A C (state).
Additional requirements :
1 Involutive Banach algebras (A , , || · ||).
2 C -algebras : ||aa || = ||a||2
B(H) (H : Hilbert space), (a) =< a, >, |||| = 1 (pure
state) GNS representation.
3 W -algebras: weakly closed subalgebra of B(H) A = A .
p1Lp(, F, P) Mm(C) : the space of random matrices of
all order moments with the normalized trace expectation: