• SANTOSH KUMAR

Articles written in Indian Academy of Sciences Conference Series

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

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.