Commutators in finite free probability, I
Jacob Campbell
TL;DR
This paper explores the expected characteristic polynomial of commutators of randomly rotated matrices within finite free probability, employing advanced combinatorial and representation theory techniques.
Contribution
It introduces a novel approach using Weingarten calculus and permutation modules to analyze commutators in finite free probability.
Findings
Derived explicit formulas for expected characteristic polynomials
Connected random matrix problems to combinatorial representation theory
Applied Weingarten calculus to finite free probability context
Abstract
This paper describes the expected characteristic polynomial of the commutator of randomly rotated matrices, in the context of the finite free probability theory initiated by Marcus, Spielman, and Srivastava. The key technical features are the use of Weingarten calculus to translate the random matrix problem into one of combinatorial representation theory, followed by some applications of the Goulden-Jackson immanant formula and the classical theory of permutation modules.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Random Matrices and Applications · Advanced Algebra and Geometry