Do Prevention and Deterrence Programs Displace Crime to Other Areas?
One concern about gun violence prevention and focused deterrence programs, especially those that concentrate on selected high-crime-intensity locations ("hot-spots"), is whether they force criminal activity to another jurisdiction. This is referred to by criminologists as "displacement."
Some researchers have found "evidence of spatial displacement of calls or crime incidents as a result of police crackdowns, especially during drug enforcement."  Others have looked for and found no displacement; for example, the Indianapolis Directed Patrol Project "led to sizable reductions in gun crime," yet "did not shift crime to surrounding areas or harm police-community relations." This study is one of the most scientifically rigorous conducted in the gun violence reduction field; however, it did not empirically study whether displacement occurred. Read more about this study in Reducing Gun Violence: Evaluation of the Indianapolis Police Department's Directed Patrol Project.
Evidence is mixed on displacement
Researchers have begun to empirically study whether gun violence reduction programs simply displace gun crime to other areas. A 2005 NIJ study that examined displacement in two crime prevention efforts in Jersey City, N.J., found not only that "crime does not seem to simply 'move around the corner'" but that offenders "resist movement to other sites both because of a natural tendency to stay with what is familiar, and because movement would demand that they encounter new and less familiar circumstances." The researchers found from interviews and field work, however, that offenders may change their methods in order to continue criminal activities without getting caught. They conclude, though, that "displacement is seldom total and often inconsequential." (pp. 8-10) Read the full report Does Crime Just Move Around the Corner? A Study of Displacement and Diffusion in Jersey City, N.J.".
Diffusion of crime control benefits seems to occur. The New Jersey study found evidence of crime reduction in areas close by, but not targeted by, the crime prevention efforts. The researchers call this "diffusion of crime control benefits" (p. 15). They found that "there appears to be strong diffusion of benefits to areas surrounding targeted locations" (p. 15), meaning outside the hot spot areas that received the intervention.
This study also found that "traditional measures of crime may miss significant elements of the displacement and diffusion phenomenon." Interviews with arrestees and ethnographic field work showed both desistance from crime and adaptation that allows continued offending resulting from the study's interventions.
More research is needed before researchers can advise on how to avoid displacement or determine the degree to which crime control efforts benefit adjacent areas, and how communities might take advantage of this phenomenon. 
 From "The Limits of Hot Spots Policing" by D. Rosenbaum, in Police Innovation: Contrasting Perspectives, ed. D. Weisburd and A. Braga, Cambridge University Press, 2006: 252-3.
 In Does Crime Just Move Around the Corner? A Study of Displacement and Diffusion in Jersey City, NJ, December 2004, NCJ 211679, Weisburd et al. list some other terms used to describe diffusion of crime control benefits, e.g., the "bonus effect," "free rider effect," "halo effect," or "multiplier effect" (see the report's introduction: 12). This report has a very readable executive summary, and the introduction to the full report lists several important studies in this area. Other quotes are from the introduction: 15-16.