We give identifications of the q-deformed Segal–Bargmann transform and define the Segal–Bargmann transform on mixed q-Gaussian variables. We prove that, when defined on the random matrix model of Śniady for… Click to show full abstract
We give identifications of the q-deformed Segal–Bargmann transform and define the Segal–Bargmann transform on mixed q-Gaussian variables. We prove that, when defined on the random matrix model of Śniady for the q-Gaussian variable, the classical Segal–Bargmann transform converges to the q-deformed Segal–Bargmann transform in the large N limit. We also show that the q-deformed Segal–Bargmann transform can be recovered as a limit of a mixture of classical and free Segal–Bargmann transform.
               
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