This is true, and I agree with your basic premise [[crime isn't heavily linked to population growth), but the issue is that the Census used a slightly different methodology in the 1990 Census and the 2010 Census, so they aren't directly comparable.
It probably isn't clear whether NYC grew faster in the 1980's or 2000's, because demographers usually agree the 2010 numbers are an undercount, as they didn't use the same imputed numbers [[guestimates of homeless, undocumented, etc.) they used in 2000 and 1990. You can see this because almost every city saw a population bump in the 2011 estimates.
Speaking generally, areas with high crime in the U.S. aren't the same as those gentrifying, so I doubt it matters that much. Whether or not there's crazy crime on the South/West sides of Chicago [[and there certainly is) hasn't put much of a damper on reviltaization in the core and North Side.
In NYC wealth and poverty are somewhat more jumbled so I can see the massive crime drops in the 1990's/2000's in places like Harlem and Bed Stuy and Bushwick as aiding gentrification somewhat, but these are exceptions.
Keep in mind too that NYC is an outlier in that it doesn't need gentrification to grow. Much of the Outer Borough growth is due to immigrants and Orthodox/Hasidic Jews [[huge families). Even if there were no gentrifiers Bed Stuy would be growing whiter because the Hasids are massively expanding into North Bed Stuy.
Somewhere like Chicago they don't get much inner city immigration anymore, and no Orthodox Jews really, so if they don't get gentrifiers they'll basically be a giant Flint. It's gentrify or die.
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