The arbitrarily varying wiretap channel - secret randomness, stability and super-activation

We study the arbitrarily varying wiretap channel (AVWC) under average error criterion when external common randomness (CR) can be used between the legitimate parties. We consider three scenarios: In the first one the CR is known to the eavesdropper, in the second it is not known to her and in the third there is no CR available. For the second scenario, we prove a complete coding theorem. For the third scenario it is known that the capacity function is discontinuous. We prove that it is nonetheless stable in the sense of being continuous around its positivity points. We characterize the points of discontinuity in terms of continuous functions. We then give a complete characterization of those pairs of AVWCs whose capacity can be super-activated in the unassisted third case - in terms of the capacity function describing the first case.