Breakdown is non-linear and dependent on many things. It depends on the geometry of the electrodes. For example a smooth, spherical electrode might have 35 kV breakdown with a 10 mm gap, but only 10 kV with a needle gap.
It also depends on air pressure. Google "Paschen curves".
For insulating materials, it somewhat follows a square root law, so 1 mm material might break down at 1 kV, but it could take 4 mm to withstand 2 kV...
According to NASA Technical Note D-7948, “inhomogeneity of leakage resistance within the body of the dielectric coupled with poor heat conductivity can produce high temperatures with attendant chemical changes. These changes can cause a decrease of resistivity by several decades of a portion of the material. The thickness of the dielectric is therefore effectively reduced and can lead to complete failure. This is the probable cause of the thickness effect-the variation of material dielectric strength with thickness in which the corona threshold voltage increases with dielectric thickness as expected, but the dielectric strength drops markedly.”