The small and large D limit of Parikh-Wilczek tunneling model for Hawking radiation

In this note, we study both the small and large dimension D limit of the tunneling model of Hawking radiation proposed by Parikh and Wilczek (2000 Phys. Rev. Lett. 85 5042). We confirm that the result is still valid for arbitrary . The sensible large D limit is given by in order to have nonzero radiation. On the other hand, the sensible small D limit is given by taking as a continuous parameter. We also explicitly show the leading order correction to the thermal radiation and discuss its connection to the two-dimensional dilaton gravity.