Work

Combinatorial aspects of Parraud’s asymptotic expansion for GUE matrices

Year: 2025

Type: article

Abstract: We give a new combinatorial proof of Parraud's formula for the asymptotic expansion in powers of 1/N 2 for the expected trace of polynomials of several independent N × N GUE matrices, which expresses the result using a mixture of free difference quotients, introducing new freely independent semicircular variables, and integration with respect to parameters.Our approach streamlines the statement of the formula while clarifying its relationship to the combinatorial genus expansion.

Source: Latin American Journal of Probability and Mathematical Statistics

DOI: 10.30757/alea.v22-22

Author: David Jekel

Institution: University of Copenhagen

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: National Science Foundation

Awards: G1233408888, PostDoctoral Research Fellowship