between 2013 and 2015, marcus, spielman and srivastava wrote a sequence of papers where they famously solved the kadison-singer problem, proved the existence of infinitely many ramanujan graphs of any fixed degree, and derived strong restricted invertibility results. with the goal of putting their results (and the results of other follow up work) under the same umbrella, we introduce amalgamated finite free probability, which is a framework that draws connections between real stable polynomials and free probability. this is joint work with nikhil srivastava.