Free Probability on the Limit C∗-Algebra Induced by a Chain of Graphs.

In this paper, we consider the limit C ∗ -algebra induced by a chain of connected finite directed graphs, and study the free probability on it. In particular, we are interested in semicircular elements in the limit C ∗ -algebra whose free distributions are the semicircular law. Our main results not only characterize free-distributional data on the limit C ∗ -algebra, but also provide a natural way to study free probabilities on “infinite” graphs. [ABSTRACT FROM AUTHOR]