The problem of violence is not with Muslim immigrants (unless they're terrorist infiltrators). The problem is with their children and grandchildren who seem to be especially vulnerable to the seductions of jihad. In fact, according to the Washington Times second generation Muslim Americans account for half of deadly terrorist attacks in the U.S.
An article at Breitbart amplifies this thesis:
For instance, Anwar al-Awlaki, the New Mexico-born jihad propagandist and “spiritual advisor” to 9/11 terrorists was the son of migrants from Yemen; Syed Farook, the Chicago-born San Bernardino terrorist was the son of Pakistani migrants; Nidal Hasan, the Fort Hood shooter was the son of a woman who emigrated from Palestine; and Muhammed Youssef Abdulazees, the Chattanooga shooter who murdered four U.S. Marines was an immigrant from Kuwait, who naturalized at the age of 6.Trump may have been characteristically hyperbolic when he declared that all Muslim immigration be stopped, but that's not to say that he's not right when he says we have a serious problem that needs to be vigorously addressed. Unfortunately, there appears to be zero inclination on the part of the federal government under this administration to address it.
In a December letter to the Obama administration demanding the release of the immigration histories of those connected to terrorism, Senator Jeff Sessions wrote: “We are dealing with an enemy that has shown it is not only capable of bypassing U.S. screening but of recruiting and radicalizing Muslim migrants after their entry to the United States. The recruitment of terrorists in the U.S. is not limited to adult migrants, but to their young children and to their U.S.-born children – which is why family immigration history is necessary to understand the nature of the threat.”
“It’s an unpleasant but unavoidable fact that bringing in large unassimilated flows of migrants from the Muslim world creates the conditions possible for radicalization and extremism to take hold, just like they’re seeing in Europe,” Sessions said on the Senate floor.