Loading Web-Font TeX/Math/Italic
| Register
\newcommand{\Cat}{{\rm Cat}} \newcommand{\A}{\mathcal A} \newcommand{\freestar}{ \framebox[7pt]{$\star$} }

2. Random matrix models with external source

    1. Random matrices with external source. More general cases


      Add remark

      Problem 2.1.

      [Pavel Bleher] Study the random matrix model with probability measure \frac{1}{Z_N}e^{-N\textrm{tr}(V(M)-AM)},
      where A is an N\times N diagonal matrix with eigenvalues \pm a (each with equal multiplicity N/2, assuming N is even), and V(M) is a general polynomial.
          A more general situation involves an external source term A with several different eigenvalues \{a_i\}_{i=1}^{j}, and multiplicities \{n_i\}_{i=1}^j, where n=n_1+n_2+\ldots+n_j. It is assumed that all limits c_j=\lim_{n\to\infty} \frac{n_j}{n} exist.

        • 2+1/2 random matrix models


          Add remark

          Problem 2.2.

          [A. Martínez-Finkelshtein] A general question about Riemann-Hilbert techniques to study the two-matrix plus external source model.

              Cite this as: AimPL: Vector equilibrium problems and random matrix models, available at http://aimpl.org/vectorequilib.