The Two-Parameter Free Unitary Segal-Bargmann Transform and its Biane-Gross-Malliavin Identification

2016/01/13 by Ching-Wei Ho, Ho, Ching-Wei · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1601.03182

openalex publication_date 2016/01/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Motivated by the two-parameter free unitary Segal-Bargmann transform in the form of conditional expectation, we derive the integral transform representation of the two-parameter free unitary Segal-Bargmann transform which coincides to the large-N limit of the two-parameter Segal-Bargmann transform on the unitary group \mathbbU(N) and explore its limiting behavior. We also extend the notion of circular systems in order to define a two-parameter free Segal-Bargmann transform and prove a version of Biane-Gross-Malliavin Theorem of the two-parameter free unitary Segal-Bargmann transform.

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