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    • Laguerre unitary ensemble to Gaussian unitary ensemble crossover: Eigenvalue statistics


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      We consider an ensemble of complex random matrices interpolating between Wishart–Laguerre and Wigner–Gaussian ensembles, and use the Dyson’s Brownian motion approach to obtain the corresponding eigenvaluestatistics. The crossover parameter ($\tau$) in this case serves as a positive-definiteness violation parameter. The joint probability density of eigenvalues of this random matrix model evolves from that of Laguerre unitary ensemble(LUE) to Gaussian unitary ensemble (GUE) as $\tau$ is varied from 0 to $\infty$. It exhibits a biorthogonal structure and hence eigenvalue correlation functions of all orders follow using a generalization of Andreief’s integration formula.

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