Are the hudud penalties to be applied to non-Muslims in Muslim lands?

Non-Muslims in Muslim lands include Dhimmis and Musta'mins, each with their own specific rulings. If a Muslim and a Dhimmi come to us for judgment, it is obligatory to rule between them. If some of them (non-Muslims) come to us for judgment among themselves, the ruler has the choice to judge between them or to ignore them. If he chooses to judge between them, he must judge according to Islamic law.

Regarding the application of hudud (prescribed punishments):

Hanafis: Hudud are applied to Dhimmis (except for the hadd of drinking alcohol) but not to Musta'mins (except for the hadd of slander). There are details concerning adultery: if a Musta'min harbi (a non-Muslim from a belligerent country) commits adultery with a Dhimmi woman, the Dhimmi woman is subject to the hadd, but the harbi is not. If a Dhimmi commits adultery with a Musta'min woman, the Dhimmi is subject to the hadd, but the Musta'min woman is not.

Malikis: The hadd of slander, theft, and murder are applied to the disbeliever and are not waived by his conversion to Islam. In cases of adultery, he is disciplined, but the hadd is not applied unless he rapes a Muslim woman, in which case he is killed, or commits sodomy, in which case he is stoned. There is no hadd on him for drinking alcohol.

Shafi'is: The Dhimmi is subjected to the hadd of adultery and theft, but not to the hadd for drinking alcohol. Islam is not a condition for the ihsan (prerequisite for stoning) for the perpetrator. The hadd for adultery is not applied to the Musta'min according to them. The disbeliever (whether Dhimmi or mu'ahid - one with a treaty) is subject to the hadd for slander.

Hanbalis: If a Dhimmi is brought before the ruler for committing a forbidden act that incurs a punishment (such as adultery, theft, slander, or murder), the hadd is applied to him. However, if he believes the act is permissible (like drinking alcohol), the hadd is not applied. The Dhimmi is subject to amputation for theft, and so is the Musta'min, according to them.