  We study correlation functions of scalar operators on the boundary of the
$AdS_3$ space deformed by moving massive particles in the context of the
AdS/CFT duality. To calculate two-point correlation functions we use the
geodesic approximation and the renormalized image method. We compare results of
the renormalized image method with direct calculations using tracing of winding
geodesics around the cone singularities, and show on examples that they are
equivalent. We demonstrate that in the geodesic approximation the correlators
exhibit a zone structure. This structure substantially depends on the mass and
velocity of the particle.
