I am looking for help pointing me in the direction of any literature or other known work that analyze the probability distribution or other important properties of random variables of the form $AB^{-1}$, where $A,B$ are independent matrix random variables whose entries from some i.i.d. random variables, such as $N(0,1)$.


I am interested in seeing what techniques have been developed for analyzing such expressions, so that I can try to see if I can adapt any of those techniques to my own problem, which involves trying to obtain probabilistic bounds on a random variable that also has the form $AB^{-1}$.



Analysis of $AB^{-1}$, where $A,B$ are random matrices
A study of the eigenvalues of $AB^{-1}$ would lead you to study solutions $\lambda$. of the equation ${\rm Det}\,(A-\lambda B)=0$. This "generalized eigenvalue problem" has been studied in some detail, see for example section 6 of [How many eigenvalues of a random matrix are real?](http://www.ams.org/journals/jams/1994-07-01/S0894-0347-1994-1231689-0/). The probability distribution of real solutions $\lambda$ is known exactly for independent standard normals $A,B$.


