One-matrix differential reformulation of two-matrix models

Brunekreef, J; Lionni, L; Thürigen, J

Research article (journal) | Peer reviewed

Abstract

Differential reformulations of field theories are often used for explicit computations. We derive a one-matrix differential formulation of two-matrix models, with the help of which it is possible to diagonalize the one- and two-matrix models using a formula by Itzykson and Zuber that allows diagonalizing differential operators with respect to matrix elements of Hermitian matrices. We detail the equivalence between the expressions obtained by diagonalizing the partition function in differential or integral formulation, which is not manifest at first glance. For one-matrix models, this requires transforming certain derivatives to variables. In the case of two-matrix models, the same computation leads to a new determinant formulation of the partition function, and we discuss potential applications to new orthogonal polynomials methods.

Details about the publication

JournalReviews in Mathematical Physics (Rev. Math. Phys.)
Volume34
Issue08
Page range2250026null
StatusPublished
Release year2022 (04/07/2022)
Language in which the publication is writtenEnglish
DOI10.1142/S0129055X2250026X
Link to the full texthttps://arxiv.org/abs/2108.00540
KeywordsRandom matrices; differential formulation; orthogonal polynomials; matrix models

Authors from the University of Münster

Thürigen, Johannes
Professur für Reine Mathematik (Prof. Wulkenhaar)