• DOI:10.1142/s2010326315500203
• Corpus ID: 119631555

Dynamical correlation functions for products of random matrices

@article{Strahov2015DynamicalCF,
  title={Dynamical correlation functions for products of random matrices},
  author={Eugene Strahov},
  journal={arXiv: Mathematical Physics},
  year={2015}
}

• E. Strahov
• Published 11 May 2015
• Mathematics, Computer Science
• arXiv: Mathematical Physics

We introduce and study a family of random processes with a discrete time related to products of random matrices. Such processes are formed by singular values of random matrix products, and the number of factors in a random matrix product plays a role of a discrete time. We consider in detail the case when the (squared) singular values of the initial random matrix form a polynomial ensemble, and the initial random matrix is multiplied by standard complex Gaussian matrices. In this case we show that the random process is a discrete-time determinantal point process. For three special cases (the case when the initial random matrix is a standard complex Gaussian matrix, the case when it is a truncated unitary matrix, or the case when it is a standard complex Gaussian matrix with a source) we compute the dynamical correlations functions explicitly, and find the hard edge scaling limits of the correlation kernels. The proofs rely on the Eynard-Mehta theorem, and on contour integral representations for the correlation kernels suitable for an asymptotic analysis.