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_μ=a_μ+a^\star_μwhere the annihilation operators a_μand creation operators a^\star_νfulfil the q-deformed commutation relation a_μa^\star_ν-q a^\star_νa_μ=Γ_{μν}, Γ_{μν} 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.

22 pages, 5 figures

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