Weingarten calculus for centered random permutation matrices
Year: 2026
Type: article
Abstract: We introduce and study the Weingarten calculus for centered random permutation matrices in the symmetric group S N . After presenting a formulation of the Weingarten calculus on the symmetric group, we derive a formula in the centered case, as well as a sign-respecting formula. Our investigations uncover the fact that a building block of this Weingarten calculus is Kummer’s confluent hypergeometric function. It allows us to derive multiple algebraic properties of the Weingarten function and uniform estimate. These results shed a conceptual light on phenomena that take place regarding the algebraic and asymptotic behavior of moments of random permutations in the resolution of Bordenave and Bordenave-Collins of strong convergence. We obtain multiple new non-trivial estimates for moments of coefficients in centered moments.
Source: Algebraic Combinatorics
DOI: 10.5802/alco.480
Authors: Benoît Collins, Manasa Nagatsu
Institution: Kyoto University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7159674822
FWCI:
Cites:
Cited by:
Related to: