Asymptotics and Statistics on Fishburn matrices

I will give a brief overview of the various types of generating functions and its applications in determining likely/unlikely behaviors of random structures. Second, I will focus on my recent work on the asymptotics and statistics of random Fishburn matrices, highlighting its connections to transformations of basic hypergeometric series and the power of a two-stage saddle-point approach in analyzing the generating functions with a sum-of-finite-product form. This is joint work with Hsien-Kuei Hwang (Academia Sinica) and Michael J. Schlosser (University of Vienna).