Determinantal Point Processes, Principal Minor Assignments, and Algebraic Graph Theory

John Urschel, Institute for Advanced Study
Fine Hall 314

In-Person and Online Talk 

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A determinantal point process (DPP) is a point process whose probability distribution is representable as the principal minors of some matrix. DPPs arise in a wide range of areas in mathematics, including combinatorics, random matrix theory, and machine learning. In this talk, we give a brief introduction to DPPs and some of their properties, and discuss the problem of recognizing when a point process is determinantal. This is a special case of the principal minor assignment problem, which, given an indexed list of prescribed values, asks if there exists a matrix with those values as its principal minors. In many cases, this question has key connections to the cycle space of a graph, a fundamental concept in algebraic graph theory.