OPE statistics from higher-point crossing

A bstract We present new asymptotic formulas for the distribution of OPE coefficients in conformal field theories. These involve products four or more and include light-light-heavy as well heavy-heavy-heavy contributions. They are derived from crossing symmetry six higher point functions on plane should be interpreted non-Gaussianities statistical coefficients. begin with a formula arbitrary operator exchanges (not necessarily primary) valid any dimension. This is first constraining d > 2. For two-dimensional CFTs, we refined stemming quasi-primaries Virasoro primaries.