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<p>We demonstrate a method to compute the limiting spectral density and the correlation kernel for 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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>-ensemble for which analytic results are not yet available.</p>

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On the solution of a class of random matrix ensembles with generalized two-body interactions and arbitrary confining potentials

  • 期刊论文

  • 发表日期：

    2026年1月27日

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  • Kazi Alam,
  • Swapnil Yadav,
  • K. A. Muttalib

摘要

We demonstrate a method to compute the limiting spectral density and the correlation kernel for 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 \(\gamma \) γ -ensemble for which analytic results are not yet available.