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

Kazi Alam; Swapnil Yadav; K. A. Muttalib

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

Mathematical Physics 2020-10-21 v1 Disordered Systems and Neural Networks Statistical Mechanics math.MP

Authors: Kazi Alam , Swapnil Yadav , K. A. Muttalib

Abstract

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.

Keywords

random matrix ensembles log-gas models biorthogonal interactions density two-point correlation functions muttalib-borodin ensembles

Cite

@article{arxiv.2010.10330,
  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 preprint arXiv:2010.10330},
  year   = {2020}
}

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13 pages

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

Abstract

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