I'm reading about sources of noise in cameras while taking images - One of them is the dark current. That is, some electrons in the CCD device of a camera are set free due to thermal noise. Those free electrons than indicate that photons have fallen on that pixel - though they haven't. Even with closed shutter, those electrons are set free. The dark current is dependent on the ambient temperature and the exposure time. [Wikipedia: Dark Current]
Now, I wonder why this behaviour is also somewhat pixel dependent. I assume that the number of released electrons should be roughly the same for all all pixels as they should average out over exposure time. In my understading this is an pyhsical application of the central limit theorem, which should result in the same "offest of light" for all pixels.
But my assumptions seem to be wrong, as this dark current stays the same for given pixels and can even be used as a finger print for a camera. A series of pictures show the same noise patterns. [Wikipedia: Fixed-Pattern_Noise]
Can someone explain why my assumptions seem to be wrong and hence why the dark current can be used as a finger print?