Gaussian Random Matrix Models for q-deformed Gaussian Random Variables

Abstract

We construct a family of random matrix models for the q-deformed Gaussian random variables G_\mu=a_\mu+a^\star_\mu where the annihilation operators a_\mu and creation operators a^\star_\nu fulfil the q-deformed commutation relation a_\mu a^\star_\nu-q a^\star_\nu a_\mu=\Gamma_{\mu\nu}, \Gamma_{\mu\nu} is the covariance and 0<q<1 is a given number. Important feature of considered random matrices is that the joint distribution of their entries is Gaussian.