Segal-Bargmann transform: the -deformation
arXiv:1703.07388 · doi:10.1007/s11005-017-1039-7
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 Śniady 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.