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

• # Fulltext

https://www.ias.ac.in/article/fulltext/conf/002/0019

• # Keywords

LUE–GUE crossover; sum of random matrices; Dyson’s Brownian motion; eigenvalue statistics; biorthogonal structure.

• # Abstract

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.

• # Author Affiliations

1. Department of Physics, Shiv Nadar University, Gautam Buddha Nagar 201 314, India