Neil Smith attempted a predictive theory of gentrification within a Marxist frame with a close examination of the phenomena in the US, particularly in NYC during the period since the word "gentrification" was coined around 1964 by Ruth Glass. Smith observes that when property values decline to its bottom, investors see an opportunity to buy low in the expectation of revalorizing the property to reach its potential. The rent gap -- the gap between the low rent of a devalued property and its potential -- opens an opportunity for capital to fill in.
The notion is at best post hoc predictive, which is to say, not predictive at all. Consider Detroit. Property values have declined, but the properties are not ipso facto an opportunity for capital to invest at the bottom under the assumption that the values can't go anywhere but up. A property's potential is not a determinable quantity.
Property potential depends on many factors: cultural or economic interest in the location; government subsidies or incentives; a housing crunch in upscale neighborhoods driving money to seek options in less upscale locations. Speculation is not one of those. Real estate has speculated on neighborhoods before without raising values. The construction of Harlem around 1900 is the most obvious case in point. Built for the wealthy, it didn't take hold and declined.
Gentrification might not be so much a reflex of capital as of policy, including zoning (creating a housing crunch, e.g.), incentives and subsidies. A too abstract economic view of gentrification will miss the role of government policies that reflect conflicting interests, especially where the owners of capital live.
One might say that as long as population grows, just about every location has a rent gap. But this does not imply that properties must decline before they achieve the gap. Neighborhoods can gentrify even if they have never declined. Glass coined the word to describe the spread of gentry, displacing and transforming working class neighborhoods. Working class neighborhoods are not all the result of decline. Some working class neighborhoods are built for the working class, and appreciate as the neighborhood grows more dense. That was certainly true of the LES in the 19th century.
The urban decline that Smith observes is more an effect of transportation than the age-decline that he attributes it to. The automobile and mass transit allowed the opening up of suburbia and the downward spiral of white flight in the 1950's and 60's.
Though it isn't stated explicitly, Smith's analysis predicts that Park Avenue should turn into the next slum. I think that's possible, but not because the buildings will age-out. Age does not entail decline. There are older buildings in Greenwich Village which attract even wealthier owners. If Park Avenue declines, it'll be because wealthy owners have been attracted to the single-family tenement. Park Avenue can't keep up with the scale of income inequality. The new New York will be full of these repurposed, culturally valued mansions that we are beginning to see in the EV. Three years ago, 47 E. 3rd was an aberration. Today there are four such single-family tenements here. Trends take a while and appear at first as insignificant. Give it time...