$$ T\overline{T} $$ Deformation of stress-tensor correlators from random geometry

We study stress-tensor correlators in the $T\bar{T}$-deformed conformal field theories two dimensions. Using random geometry approach to $T\bar{T}$ deformation, we develop a geometrical method compute correlators. More specifically, derive deformation Polyakov-Liouville anomaly action and calculate three four-point first-order from deformed action. The results are checked against standard perturbation theory computation further check consistency with operator product expansions of stress tensor. A salient feature is logarithmic correction that absent three-point functions but starts appearing function.