# nLab free probability

Free probability is a noncommutative analogue of the probability theory introduced by Dan Voiculescu around 1990 and having some precursors in earlier works on random matrices by Freeman Dyson and others.

• D. V. Voiculescu, Free Probability Theory: Random Matrices and von Neumann Algebras, Proc. ICM 1994 pdf

• D.V. Voiculescu, K.J. Dykema, A. Nica. Free random variables, CRM Monograph Series, vol. 1, Amer. Math. Soc. 1992.

• D.V. Voiculescu, Limit laws for random matrices and free products, Inventiones Mathematicae 104:201–220, 1991.

• D.V. Voiculescu, Symmetries of some reduced free product $C^\ast$-algebras, in Operator algebras and their connections with topology and ergodic theory (Bucsteni, 1983), Lecture Notes in Math. 1132, 556–588. Springer 1985.

• A. Nica, R. Speicher, Lectures on the combinatorics of free probability, Cambridge University Press, 2006

• Terrence Tao, notes on free probability, blog entry

• wikipedia free probability

• Michael Hartglass, Free product $C^\ast$-algebras associated to graphs, free differentials, and laws of loops, arxiv/1509.02553

• Roland Friedrich, John McKay, Formal groups, Witt vectors and free probability, arxiv/1204.6522; Homogeneous Lie groups and quantum probability, arxiv/1506.07089