  An identity of Szego, and a volume calculation, heuristically suggest a
simple expression for the distribution of Verblunsky coefficients with respect
to the (normalized) exponential of the $S^1$ trace of the Gaussian free field.
This heuristic expression is not quite correct. A proof of the correct formula
has been found by Chhaibi and Najnudel. Their proof uses random matrix theory
and overcomes many difficult technical issues. In addition to presenting the
Szego perspective, we show that the Chhaibi and Najnudel theorem implies a
family of combinatorial identities (for moments of measures) which are of
intrinsic interest.
