There is a well-documented theory for breakdown voltage vs pressure in the form of Paschen's law.
But what is the trend of the electrical resistivity of air as a function of the electric field imposed on it? It is quite difficult to find such a curve.
Also, is there a minimum resistivity for arcing, i.e a breakdown is assumed to have taken place?
I understand that there are two questions in this, but I guess it will be allowed considering that the two are linked.