The average density of states in the Gaussian ensembles whose eigenvalues are restricted to lie in a given interval, or to be creatergreater than a given minimal value, was calculated by Dean and Majumdar in Extreme Value Statistics of Eigenvalues of Gaussian Random Matrices. The eigenvalue density has a $1/\sqrt x$ divergence at the end points of the interval. The case in the OP of a constraint of positive eigenvalues is the red solid curve in this plot from the cited paper.
The average density of states in the Gaussian ensembles whose eigenvalues are restricted to lie in a given interval, or to be creater than a given minimal value, was calculated by Dean and Majumdar in Extreme Value Statistics of Eigenvalues of Gaussian Random Matrices. The eigenvalue density has a $1/\sqrt x$ divergence at the end points of the interval. The case in the OP of a constraint of positive eigenvalues is the red solid curve in this plot from the cited paper.
The average density of states in the Gaussian ensembles whose eigenvalues are restricted to lie in a given interval, or to be greater than a given minimal value, was calculated by Dean and Majumdar in Extreme Value Statistics of Eigenvalues of Gaussian Random Matrices. The eigenvalue density has a $1/\sqrt x$ divergence at the end points of the interval. The case in the OP of a constraint of positive eigenvalues is the red solid curve in this plot from the cited paper.
The average density of states in the Gaussian ensembles whose eigenvalues are restricted to lie in a given interval, or to be creater than a given minimal value, was calculated by Dean and Majumdar in Extreme Value Statistics of Eigenvalues of Gaussian Random Matrices. The eigenvalue density has a $1/\sqrt x$ divergence at the end points of the interval. The case in the OP of a constraint of positive eigenvalues is the red solid curve in this plot from the cited paper.
