Combinatorics of the Berezin-Karpelevich Integral
Jonathan Novak
TL;DR
This paper explores the combinatorial structure of the Berezin-Karpelevich integral, revealing its expansion in terms of monotone Hurwitz numbers and deriving related combinatorial identities.
Contribution
It introduces a topological expansion of the Berezin-Karpelevich integral using monotone Hurwitz numbers, connecting matrix integrals with combinatorial enumeration.
Findings
Topological expansion of the Berezin-Karpelevich integral in terms of monotone Hurwitz numbers
Derivation of new combinatorial identities related to the integral
Establishment of connections between matrix integrals and combinatorial structures
Abstract
The Berezin-Karpelevich integral is a double integral over unitary matrices which plays the role of the Itzykson-Zuber integral in rectangular matrix models. We obtain a topological expansion of the Berezin-Karpelevich integral in terms of monotone Hurwitz numbers, and obtain from this certain combinatorial identities.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsTopological and Geometric Data Analysis · Mathematical Dynamics and Fractals · advanced mathematical theories