  Biane proved the free analog of the logarithmic Sobolev inequality for
probability measures on the real line by means of random matrix approximation
procedure. We show that the same method can be applied to reprove Biane and
Voiculescu's free analog of Talagrand's transportation cost inequality for
measures on the real line. Furthermore, we prove the free analogs of the
logarithmic Sobolev inequality and the transportation cost inequality for
measures on 1-dimensional torus as well by extending the method to special
unitary random matrices.
