Matrix-Model Approach to Electron Correlations in a Strong Magnetic Field
The lowest Landau level of the two dimensional electron in a strong magnetic field is investigated by the random matrix model technique. We discuss the universality of the electron correlation of the edge state for the arbitrary polynomial measure form of the eigenvalue, based upon the large N limit of the matrix formulations. The edge state is described by the c = 1 conformal field theory. The relation of the matrix model to the 2D quantum gravity is discussed. It is shown that a matrix model which describes the lowest Landau level state with an appropriate interaction becomes a new model of the 2D quantum gravity coupled to matter field with the central charge c = 1.
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