Among various types of noncommutative probability, free
probability is particularly compatible with classical probability
theory via random matrix theory. However, there are several ways to
describe the correspondence, which are not identical. Previously, the
speaker and collaborators have mainly focused on the correspondence
given by the Bercovici–Pata bijection. In recent work, we have
considered another correspondence known as "potential correspondence,"
which is familiar well with concepts such as Voiculescu's free
entropy, and obtained new results based on this viewpoint.
In this talk, we first introduce the concept of potential
correspondence by reviewing known results. Subsequently, we present
our new results obtained through this framework. This work is based on
joint work with Yuki Ueda (Hokkaido University of Education,
Asahikawa).