Skip to Main content Skip to Navigation
Conference papers

A note on moments of derivatives of characteristic polynomials

Abstract : We present a simple technique to compute moments of derivatives of unitary characteristic polynomials. The first part of the technique relies on an idea of Bump and Gamburd: it uses orthonormality of Schur functions over unitary groups to compute matrix averages of characteristic polynomials. In order to consider derivatives of those polynomials, we here need the added strength of the Generalized Binomial Theorem of Okounkov and Olshanski. This result is very natural as it provides coefficients for the Taylor expansions of Schur functions, in terms of shifted Schur functions. The answer is finally given as a sum over partitions of functions of the contents. One can also obtain alternative expressions involving hypergeometric functions of matrix arguments.
Complete list of metadata

Cited literature [24 references]  Display  Hide  Download
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Monday, August 24, 2015 - 3:45:05 PM
Last modification on : Thursday, May 27, 2021 - 1:54:05 PM
Long-term archiving on: : Wednesday, November 25, 2015 - 4:52:06 PM


Publisher files allowed on an open archive




Paul-Olivier Dehaye. A note on moments of derivatives of characteristic polynomials. 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, San Francisco, United States. pp.681-692, ⟨10.46298/dmtcs.2823⟩. ⟨hal-01186251⟩



Record views


Files downloads