If I acknowledge that some communities are more likely to live their daily lives under these three factors altogether, it could explain why these communities may be more vulnerable to daily life challenges, and more easily resort to violence. Still, that doesn't give me a causal link between racial/cultural diversity and violence, far from it, but I can understand why those who prefer taking shortcuts may end up reaching this conclusion.
This shortcut is also very comfortable for the peace of mind: once I attribute violence to racial/cultural diversity, I can also safely conclude that I will never be part of the problem (if I consider myself as being part of the "good" racial/cultural group)...
I have noticed a very very very strong correlation of how dangerous it can be just to walk outside alone, or at night, or walk in public with your cellphone. I believe there is a link between violence and race and culture.
I am sorry to ask but I have the feeling that something is missing in your comment. You said you have lived in poor areas and observed violence, or did you mean that you witnessed violence only in a subset of the areas you listed?