• Corpus ID: 224803500

# On the computation of density and two-point correlation functions of a class of random matrix ensembles

@article{Alam2020OnTC,
title={On the computation of density and two-point correlation functions of a class of random matrix ensembles},
author={Kazi Alam and Swapnil Yadav and K. A. Muttalib},
journal={arXiv: Mathematical Physics},
year={2020}
}
• Published 18 October 2020
• Mathematics
• arXiv: Mathematical Physics
We demonstrate a method to solve a general class of random matrix ensembles numerically. The method is suitable for solving log-gas models with biorthogonal type two-body interactions and arbitrary potentials. We reproduce standard results for a variety of well-known ensembles and show some new results for the Muttalib-Borodin ensembles and recently introduced $\gamma$-ensemble for which analytic results are not yet available.

## References

SHOWING 1-10 OF 45 REFERENCES
Generalized random matrix model with additional interactions
• Mathematics, Physics
Journal of Physics A: Mathematical and Theoretical
• 2019
We introduce a log-gas model that is a generalization of a random matrix ensemble with an additional interaction, whose strength depends on a parameter . The equilibrium density is computed by
New family of unitary random matrices.
• Mathematics
Physical review letters
• 1993
An exactly solvable random matrix model related to the random transfer matrix model for disordered conductors that crosses over from a Wigner to a distribution which is increasingly more Poisson-like, a feature common to a wide variety of physical systems including disorder and chaos.
Deformed Cauchy random matrix ensembles and large N phase transitions
We study a new hermitian one-matrix model containing a logarithmic Penner's type term and another term, which can be obtained as a limit from logarithmic terms. For small coupling, the potential has
Energy correlations for a random matrix model of disordered bosons
• Physics
• 2006
Linearizing the Heisenberg equations of motion around the ground state of an interacting quantum many-body system, one gets a time-evolution generator in the positive cone of a real symplectic Lie
Multiple orthogonal polynomial ensembles
Multiple orthogonal polynomials are traditionally studied because of their connections to number theory and approximation theory. In recent years they were found to be connected to certain models in
Muttalib--Borodin ensembles in random matrix theory --- realisations and correlation functions
• Mathematics
• 2015
Muttalib--Borodin ensembles are characterised by the pair interaction term in the eigenvalue probability density function being of the form $\prod_{1 \le j 0$, realisations in terms of the eigenvalue
Biorthogonal ensembles with two-particle interactions
• Mathematics
• 2014
We investigate determinantal point processes on [0, +∞) of the form We prove that the biorthogonal polynomials associated with such models satisfy a recurrence relation and a Christoffel–Darboux
Level spacings at the metal-insulator transition in the Anderson Hamiltonians and multifractal random matrix ensembles
We consider orthogonal, unitary, and symplectic ensembles of random matrices with $(1/a)(\mathrm{ln}{x)}^{2}$ potentials, which obey spectral statistics different from the Wigner-Dyson and are argued
Random matrix models with additional interactions
It has been argued that, despite remarkable success, existing random matrix theories are not adequate at describing disordered conductors in the metallic regime, due to the presence of certain