Pearcey Kernel Basis:
Beyond Second Order Differential Equations

There is a well-known connection between orthogonal polynomials, second-order Sturm-Liouville differential equations, random matrices, and orthogonal projectors in \( L_2 \). This post explores an extension of this topic. We have identified a basis for the Pearcey Kernel, initially introduced by Brezin and Hikami . To achieve this, we move beyond the traditional approach of second-order differential equations and orthogonal polynomials, employing third-order equations and biorthogonal bases instead.

published 8.04.2021, last update 24.06.2024