  We use random walks to simulate the fluid limit of two coupled diffusive
limit order books to model correlation emergence. The model implements the
arrival, cancellation and diffusion of orders coupled by a pairs trader
profiting from the mean-reversion between the two order books in the fluid
limit for a Lit order book with vanishing boundary conditions and order volume
conservation. We are able to demonstrate the recovery of an Epps effect from
this. We discuss how various stylised facts depend on the model parameters and
the numerical scheme and discuss the various strengths and weaknesses of the
approach. We demonstrate how the Epps effect depends on different choices of
time and price discretisation. This shows how an Epps effect can emerge without
recourse to market microstructure noise relative to a latent model but can
rather be viewed as an emergent property arising from trader interactions in a
world of asynchronous events.
