Yes - and you'll see poverty, drug use and low educational attainment are all far more highly correlated with criminal activity, especially violent crime, than race is.
Now minorities are more likley to be poor and less well educated than whites are (note this is in neither case a blanket statement, merely one of probability. I am more than a bit aware that rural Appalachia is largely white and Clarence Thomas is both richer and better educated than I am). Why is that? Well consider that until 40 years ago blacks weren't even allowed to be educated in the vast majority of halfway decent schools, faced legal discrimination for any kind of work and amenities, etc., and it might explain why we have a poor and relatively uneducated population of parents creating the generation currently in their prime. We know also how strongly parental income and education correlates to that of the child right? (again exceptions occur on both sides - my own parents were a bus driver and a house cleaner) so what does that say for the likelihood of the current generation of blacks avoiding the poverty and education trap?
You see that crap is self perpetuating. Not only do you have a greater probability that your parents do not care about education and cannot afford the resources to help you take best advantage of yours, but the chances are they are more likely to live in a school district that has the worst teachers, worst equipment, etc etc. Nothing correlates better to the drugs/crime/poverty trifecta than low education. Sure exceptions occur here too - we all know people both whte and black that have risen up out of such backgrounds through sheer intellect and force of will. But probabilities don't lie. Crap schools = crap education = poverty = crime. Hard to say otherwise really. Prisons aren't all that full of Mensa members with six-figure incomes (although in some cases they probably should be!).
I'm focusing on blacks because I know the data better. I can infer that it applies to most immigrants (especially when you throw in a language barrier too) but am not as familiar with numbers and studies that support this.
So next time you see a police blotter with lots of Tayshauns and Josés in it, start looking at where they lived and went to school. Look and see if their parents were given a chance at a decent life. Now on an individual level that in no way excuses a criminal - I do NOT buy the excuse that an underprivileged upbringing in any way, even slightly, excuses a life of crime. It just makes it a damn sight more likely. Remember - they said the same things about the Irish too.