That's called the 'contact hypothesis'. There's been a few studies that support it (including a famous one involving WWII soldiers' attitudes to mixed-race platoons) but most social science research has found the opposite.

Robert Putnam is the political scientist who's done the most work on this, and if you're curious, his most relevant paper is probably 'E Pluribus Unum: Diversity and Community in the Twenty-first Century'.

Putnam is an interesting academic - he was (and still is, I believe) utterly dismayed by the results of his research, but decided to publish it anyway.

> I would have thought proximity could also ease tension if there is a degree of integration.

It might, but racial proximity in America often doesn't involve much integration, it is proximity of communities segregated by a combination of voluntary choice and informal discrimination. On the black/white divide specifically, there are in many areas strong cultural forces on both sides working against integration, and making it so that proximity increases conflict which reinforces hostile attitudes on both sides.