  We describe how a model of effective interactions between quantum
fluctuations under certain assumptions can be constructed in a way so that the
large-scale limit gives an effective theory that matches general relativity in
vacuum regions. This is an investigation of a possible scenario of spacetime
emergence from quantum interactions directly in the spacetime, and of how
effective quantum behaviour might provide a useful link between detailed
properties of quantum interactions and general relativity. The quantum
fluctuations are assumed to entangle sufficiently for a cohesive spacetime to
form, so that their effective properties can be described relative to a
D-dimensional reference frame. To obtain the desired features of a smooth
metric with a vanishing Ricci tensor, the quantum fluctuations are modelled as
Gaussian probability distributions, with a shape set relative to the
interactions coming from the surroundings. At small scales, the propagation
through the spacetime is modelled by a Gaussian random walk.
