Segal-Bargmann transform: the $q$-deformation
Probability
2018-01-17 v1 Mathematical Physics
Functional Analysis
math.MP
Abstract
We give identifications of the -deformed Segal-Bargmann transform and define the Segal-Bargmann transform on mixed -Gaussian variables. We prove that, when defined on the random matrix model of \'Sniady for the -Gaussian variable, the classical Segal-Bargmann transform converges to the -deformed Segal-Bargmann transform in the large limit. We also show that the -deformed Segal-Bargmann transform can be recovered as a limit of a mixture of classical and free Segal-Bargmann transform.
Cite
@article{arxiv.1703.07388,
title = {Segal-Bargmann transform: the $q$-deformation},
author = {Guillaume Cébron and Ching-Wei Ho},
journal= {arXiv preprint arXiv:1703.07388},
year = {2018}
}