  We study quantum spacetime fluctuations near light-sheet horizons associated
with a Rindler wedge in AdS spacetime, in the context of AdS/CFT. In
particular, we solve the vacuum Einstein equation near the light-sheet horizon,
augmented with the Ansatz of a quantum source smeared out in a Planckian width
along one of the light-cone directions. Such a source, whose physical
interpretation is of gravitational shockwaves created by vacuum energy
fluctuations, alters the Einstein equation to a stochastic partial differential
equation taking the form of a Langevin equation. By integrating fluctuations
along the light sheet, we find an accumulated effect in the round-trip time of
a photon to traverse the horizon of the Rindler wedge that depends on both the
$d$-dimensional Newton constant $G_N^{(d)}$ and the AdS curvature $L$, in
agreement with previous literature utilizing different methods.
