Folkmar Bornemann

collaborators

4 papers

math.PR2026

Asymptotic Expansions of Gaussian and Laguerre Ensembles at the Soft Edge III: Generating Functions

Folkmar Bornemann

We conclude our work [arXiv:2403.07628, arXiv:2503.12644] on asymptotic expansions at the soft edge for the classical $n$ -dimensional Gaussian and Laguerre ensembles, now studying…

math.PR2025

Asymptotic Expansions of Gaussian and Laguerre Ensembles at the Soft Edge II: Level Densities

Folkmar Bornemann

We continue our work [arXiv:2403.07628] on asymptotic expansions at the soft edge for the classical $n$ -dimensional Gaussian and Laguerre random matrix ensembles. By revisiting the…

math.CA2025

Algebraic Independence of an Airy Function, Its Derivative, and Antiderivative

Folkmar Bornemann

Using tools from the Siegel-Shidlovskii theory of transcendental numbers, we prove that a nontrivial solution of the Airy equation, its derivative, and an antiderivative are algebr…

math.PR2025

Asymptotic Expansions of the Limit Laws of Gaussian and Laguerre (Wishart) Ensembles at the Soft Edge

Folkmar Bornemann

The large-matrix limit laws of the rescaled largest eigenvalue of the orthogonal, unitary, and symplectic $n$ -dimensional Gaussian ensembles -- and of the corresponding Laguerre en…