Return of the Blood Libel

if we look across America there is a correlation between violent crime and the prevalence of undocumented immigrants — a negative correlation. That is, places with a lot of immigrants, legal and undocumented, tend to have exceptionally low crime rates. The poster child for this tale of un-carnage is the biggest city of them all: New York, where more than a third of the population is foreign-born, probably including around half a million undocumented immigrants — and crime has fallen to levels not seen since the 1950s.
via Return of the Blood Libel
There is no immigration crime wave.