I hope that you will forgive the shameless self-promotion, but I recently published a paper in Sociological Science (yay open access!) that examined neighborhood racial change in New York, Los Angeles, Chicago, and Houston metropolitan neighborhoods with an amazingly talented colleague, Siri Warkentien.
We find mixed results related to future racial integration. On the negative side we find that recent estimates overestimate the stability of long-term racial integration. Previous studies don't really examine the pace of neighborhood change, which reveals many integrated neighborhoods are in fact resegregating.
On a more positive note, we find that some neighborhoods really do maintain multiethnic segregation over many decades. We call those neighborhoods "quadrivial ...