Gentrification Reducing Downward Mobility?

I really wish the findings of a Pew Trust report (PDF) regarding economic mobility was a little clearer. The best I could figure, before they threw in the math equation, which totally lost me, is that when a neighborhood decreases poverty a child’s chance of heading downward as he/she grows up decreases. Yeah, there are a lot of negatives, unfortunately it isn’t clear when you make the sentence positive that there is the data to back it up. A positive sentence would be that when a neighborhood becomes richer, or parents move into a neighborhood with less than 10-20% poverty, their children will grow up to become successful adults who make more money than their parents. What was clear was a child growing up in a poorer neighborhood where poverty was 20% or more is more likely to become poorer.
I was reading the report trying to figure out if gentrification, or the lessening of the rate of poverty in a neighborhood, had any positive for poor children who remain in the neighborhood. The best I can figure from the report is that it doesn’t hurt. Apparently there weren’t enough families in the study group who moved from poor neighborhoods to neighborhoods with less than 10% poverty whose children became upwardly mobile adults.