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| -rw-r--r-- | bezout.tex | 10 |
1 files changed, 6 insertions, 4 deletions
@@ -152,10 +152,12 @@ is shifted by $p\epsilon$. The eigenvalue spectrum of the Hessian of the real part, or equivalently the eigenvalue spectrum of $(\partial\partial H)^\dagger\partial\partial H$, is the -singular value spectrum of $\partial\partial H$. This is a more difficult -problem and to our knowledge a closed form for arbitrary $\kappa$ is not known. -We have worked out an implicit form for this spectrum using the saddle point of -a replica calculation for the Green function. blah blah blah\dots +singular value spectrum of $\partial\partial H$. When $\kappa=0$ and the +elements of $J$ are standard complex normal, this corresponds to a complex +Wishart distribution. For $\kappa\neq0$ the problem changes, and to our +knowledge a closed form is not known. We have worked out an implicit form for +this spectrum using the saddle point of a replica calculation for the Green +function. blah blah blah\dots The transition from a one-cut to two-cut singular value spectrum naturally corresponds to the origin leaving the support of the eigenvalue spectrum. |