Electric field required to split water into oxygen and hydrogen Others sources typically say that the minimum voltage required to split water into hydrogen and oxygen is 1.229 V. Overvoltage is typically required in a practical device due to inefficiency leading to heat production. 

However, suppose that two electrodes are separated by a large distance.  This will result in a very low electric field strength (generally, electric field equals $V/d$ where $d$ is the distance of separation).  Is there a threshold electric field level required for electrolysis to take place?
In part, there is no abrupt cutoff because the gradient of the field is not spread evenly across the electrolyte: the gradient is steep at the interface between electrodes and the electrolyte, where gas evolution actually takes place, not in the body of the electrolyte. Note where bubbles arise in this video.

However, if the conductivity of the electrolyte is low, whether due to electrode separation or low ionization, then electrolysis proceeds more slowly, perhaps imperceptibly, though there is no complete cutoff point.