  We study correlation functions of the probabilistic Schwarzian Field Theory.
We compute cross-ratio correlation functions exactly in the case when the
corresponding Wilson lines do not intersect, confirming predictions made in the
physics literature via limit of the conformal bootstrap and the DOZZ formula.
Moreover, we prove that these correlation functions characterise the measure
uniquely. We use them to define and compute the stress-energy tensor
correlation functions, and demonstrate, in particular, that these agree with
the results obtained earlier by formal differentiation of the partition
function.
