A Why is this Pilot-wave model on a discrete spacetime stochastic?

[Ali Lavasani]

Look at the paper in the link below:
https://link.springer.com/content/pdf/10.1007/s10701-016-0026-7.pdf
It introduces a pilot-wave model on a discrete spacetime lattice. However, the pilot-wave model is not deterministic; the motion of quantum particles is described by a |Ψ|^2-distributed Markov chain. It mentions that "Introducing Markovian process is crucial, if time is discretized" and "The discreteness is by itself responsible for the randomness of the motion on the basic level".

My question is, WHY must a Bohmian model be stochastic if the space and time are discrete, in other words, what happens if one tries to simply generalize the commonplace deterministic Bohmian mechanics to the case in which the spacetime is a discrete lattice?

 

[Demystifier]

Bohmian mechanics certainly does not necessarily need to be stochastic when space and time are discrete. But if you want it to be deterministic, then there is more than one way to do it, so the theory is not unique.

 

[Ali Lavasani]

This is another thing they have mentioned:

The transformation of a discrete distribution|t0|^2, e.g. at the slits, into the discrete distribution|t|^2, e.g. far from the slits, cannot be made in a non-stochastic manner, as it would require transitions from every (initial or intermediate) state into a single subsequent state."

Of course there might be several ways to define a deterministic Bohmian theory on a discrete spacetime, but what are these ways? My question was, why we would fail if we just repeat what we did in the continuous spacetime in the discrete one, without any change? What's the reason they have invoked stochasticity, what requirement has it fulfilled?