Correlators In The Beta-Deformed Gaussian Hermitian And Complex Matrix Models

We investigate the beta-deformed Gaussian Hermitian and N x N complex matrix models which are defined as the eigenvalue integral representations. Their W-1(+infinity) constraints are constructed such that the constraint operators yield the same W-1(+infinity) n-algebra. When particularized to the Virasoro constraints in the W-1(+infinity) constraints, the corresponding constraint operators yield the Witt algebra and null 3-algebra. By solving our Virasoro constraints, we derive the formulas for correlators in these two beta-deformed matrix models, respectively.