There are a number of reasons for the decrease in crime in the 1990s, including a decrease in the use of crack cocaine and, famously, lead removal (http://www.motherjones.com/environment/2013/01/lead-crime-li...). Causation/correlation, etc.
The same thing is happening in many "gentrifying" cities. Crime goes down in DC as the rates in neighboring counties in Maryland increase.
You get a fantastic correlation between section 8 housing and crime. Eliminating a ton of crime is not very complicated and doesn't require much police work. You just deport all the poor people. That's effectively what happened under Giuliani.