I am not familiar with economic study on gentrification, but there are many studies on urban redevelopment, especially its dynamic impact on urban structure.  One classic paper is called "Stochastic City" (sorry I forgot the author's name). William Wheaton also published papers on urban redevelopment (again, sorry I forgot the papers' titles).  Hope this information might be of some use to you.

Relevant papers introducing the perspective of urban economists on gentrification are:

Glaeser et al.: Consumer City

scholar.harvard.edu/files/glaeser/files/consumer_city.pdf

Glaeser homepage: http://scholar.harvard.edu/glaeser/home

A policy-oriented economic view:

https://www.google.de/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&ved=0ahUKEwiepv3R3rHPAhWMnRoKHSujAg0QFgg3MAI&url=http%3A%2F%2Fweb.williams.edu%2FEconomics%2FArtsEcon%2Flibrary%2Fpdfs%2FWhyIsGentrificationAProbREFORM.pdf&usg=AFQjCNGoBfmSv81ElPQt1NKBmSh0L72LHw&cad=rja

A journal article presenting the up-to-date debate on gentrification in the US:

http://cultureandyouth.org/poverty/articles-poverty/the-economics-of-gentrification-2/

Kind regards

Peter

Although I am not sure, some economists might refer to this as filtering-up. This might be useful for a literature search.

Gentrification is something like segregation. Perhaps the tipping point literature is relevant. Have you seen this? https://sites.google.com/site/agilleyschellingmodel/

A Google Scholar search of "economics of gentrification" points to many case-study cities.

I found the following usefull, but there is indeed not much that takes an economic persepctive

Understanding Gentrification: a Case Study Approach

http://wesscholar.wesleyan.edu/etd_hon_theses/1677/

https://www.researchgate.net/profile/George_Ann_Ryan/publication/318298803_The_Impact_of_Rapid_Gentrification_on_Rents/links/596106f2a6fdccc9b1077243/The-Impact-of-Rapid-Gentrification-on-Rents.pdf

Miller, M. M. (2017). Essays in Urban and Labor Economics (Doctoral dissertation, University of California, Los Angeles). http://escholarship.org/uc/item/31h3b0mp.pdf

Lidia Diappi (auth.), Lidia Diappi (eds.)

Emergent Phenomena in Housing Markets: Gentrification, Housing Search, Polarization [1 ed.]

978-3-7908-2863-4, 978-3-7908-2864-1

Physica-Verlag Heidelberg

2013

Thesis The Impact of Rapid Gentrification on Rents