How deep is the permafrost in the Antarctic?
According to "Permafrost, active-layer dynamics and periglacial environments of continental Antarctica" South African Journal of Science 98. pages 82-90:

Only 25% of Antarctica has permafrost, as the material beneath thick ice sheets is not permafrost. 

The deepest permafrost occurs where there is no ice sheet. 

The deepest permafrost in the Antarctic is about 1000m.