Robert VanBruggen, budding writer for National Interest, discovered in running a few correlations that while diversity (as calculated using the Ethno-Linguistic Fragmentation index) and incarceration rates are meaningfully related in the developed world, murder rates are not. The wide variance by country in what lands one in jail renders criminality statistics based on incarceration rates unsatisfactory. Murder, which is unlikely to go unreported, serves as a decent proxy for the total violent crime rate in a country. So what he has apparently highlighted is that more ethnically and linguistically diverse nations are more likely to have harsher rules on social conduct than homogenuous ones are. Multiculturalism at work--differing social mores and lifestyle expectations mean less toleration of each of them for the sake of retaining cohesion at the expense of personal freedoms.
But a diversity index isn't an optimal measure of anything. I've tried creating a couple of my own diversity indices but they've consistently been far less predictive of conditions than simply looking at race. To understand why, consider San Diego, East St. Louis, and Leawood--by a measure of ethnic/racial diversity, San Diego will always come out as being the most diverse, while East St. Louis and Leawood will register as being similarly quite homogenuous. But in measures of social pathology, the homogenuous East St. Louis and Leawood will be at opposite ends of the spectrum, with San Diego bemusingly in the middle. If we just look at the percentage of the population in each city that is non-Hispanic white, things suddenly make a lot more sense. That East St. Louis and Leawood are both ethnically homogenuous is about the only thing the two have in common.
Attacking balkanization as a universal problem specific to say, London, carries less political risk than pointing out the poor performance of Central Asian Muslims there. How things are mixed does matter (creating feelings of resentment, etc), but the ingredients themselves are of paramount importance. I suspect the language your neighbor speaks has less to do with how likely he is to kill someone than who his ancestors were.
Unfortunately, most countries don't release demographic data broken down by race or ethnicity, so quantitative comparisons are much more difficult to make than they need be. Last year, I responded to the tendentious paper written by Gregory Paul claiming that America's religiosity was somehow the cause of its social pathologies compared to a secular Europe. Of course, the countries across the Atlantic do not have to deal with a population that is one-eighth black (and one-eighth Latin American Hispanic). By finding the frequency of behavior in whites in the US on the various measures Paul used (teen pregnancy, murder, etc) and pretending American blacks acted in the same way as American whites, I showed that the US would be in the thick of the European pack if not for its demographic disadvantages.
Robert didn't include the US in the numbers he ran due to its astronomically high incarceration rate of 738 per 100,000 with the next closest country a diminutive 193. But the non-Hispanic white US incarceration rate is only 230--higher than comparative developed nations due to tough sentencing especially with regards to drug use and possession, but not astonishingly so.