  We present a rigorous proof of the Dorn, Otto, Zamolodchikov, Zamolodchikov
formula (the DOZZ formula) for the 3 point structure constants of Liouville
Conformal Field Theory (LCFT) starting from a rigorous probabilistic
construction of the functional integral defining LCFT given earlier by the
authors and David. A crucial ingredient in our argument is a probabilistic
derivation of the reflection relation in LCFT based on a refined tail analysis
of Gaussian multiplicative chaos measures.
