  We studied the evolution of Wightman correlator in a thermalizing state
modeled by AdS_3-Vaidya background. We gave a prescription for calculating
Wightman correlator in coordinate space without using any approximation. For
equal-time correlator $\langle O(v,x)O(v,0)\rangle$, we obtained an enhancement
factor $v^2$ due to long range correlation present in the initial state. This
was missed by previous studies based on geodesic approximation. We found that
the long range correlation in initial state does not lead to significant
modification to thermalization time as compared to known results with generic
initial state. We also studied spatially integrated Wightman correlator and
showed evidence on the distinction between long distance and small momentum
physics for an out-of-equilibrium state. We also calculated radiation spectrum
of particle weakly coupled to $O$ and found lower frequency mode approaches
thermal spectrum faster than high frequency mode.
