The Ginibre Ensemble and Gaussian Analytic Functions
Manjunath Krishnapur, Bálint Virág
Source abstract
Abstract We show that as n changes, the characteristic polynomial of the n×n random matrix with i.i.d. complex Gaussian entries can be described recursively through a process analogous to Pólya’s urn scheme. As a result, we get a random analytic function in the limit, which is given by a mixture of Gaussian analytic functions. This suggests another reason why the zeros of Gaussian analytic functions and the Ginibre ensemble exhibit similar local repulsion, but different global behavior. Our approach gives new explicit formulas for the limiting analytic function.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.