RALEIGH, N.C. — In the African-American neighborhoods near downtown Raleigh, the playfully painted doors signal what’s coming. Colored in crimson, in coral, in sea foam, the doors accent newly renovated Craftsman cottages and boxy modern homes that have replaced vacant lots. To longtime residents, the doors mean higher home prices ahead, more investors knocking, more white neighbors. Here, and in the center of cities across the United States, a kind of demographic change most often associated with gentrifying parts of New York and Washington has been accelerating. White residents are increasingly moving into nonwhite neighborhoods, largely African-American ones. In America, racial diversity has much more often come to white neighborhoods. Between 1980 and 2000, more than 98 percent of census tracts that grew more diverse did so in that way, as Hispanic, Asian-American, and African-American families settled in neighborhoods that were once predominantly white. But since 2000, … [Read more...] about The neighborhood is mostly black. The buyers are mostly white.