Biorthogonal ensembles of derivative type
Mathematical Physics
2026-03-05 v2 math.MP
Probability
Abstract
In this paper, we prove that biorthogonal ensembles on the real line with a specific derivative structure admit an explicit correlation kernel of double contour integral form. We will demonstrate that this expression is a valuable starting point for asymptotic analysis and that our class of biorthogonal ensembles admits a large variety of limit kernels, by proving that two new classes of limit kernels can occur. The first type is a deformation of the hard edge Bessel kernel which arises in polynomial ensembles describing the eigenvalues of the sum of two random matrices, while the second type arises for Muttalib-Borodin type deformations of polynomial ensembles.
Cite
@article{arxiv.2601.18427,
title = {Biorthogonal ensembles of derivative type},
author = {Tom Claeys and Jiyuan Zhang},
journal= {arXiv preprint arXiv:2601.18427},
year = {2026}
}