Here is a link to a twitter thread by one of the authors
This paper by K. Hunter Wapman, Sam Zhang, Aaron Clauset, & Daniel B. Larremore evaluates the dynamics of various aspects of academia hiring in the US, and the extreme inequalities of this process. In a section of this study, they also find that while there are gains for women’s representation in academia in most subjects, these improvements are mostly a result of demographic turnover and earlier hiring changes. Thus, they suggest, that without further changes long-term gender parity in most fields will likely not be achieved.
They also have numerous other findings, such as that a small set of universities produce most of the US-hired professors, and that there is a higher attrition rate among non-US trained faculty.