From 6b572dca1c4e53537352d9d4b09fccb637f392c9 Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Mon, 7 Dec 2020 18:59:20 +0100 Subject: Make reference to complex Wishart. --- bezout.tex | 10 ++++++---- 1 file changed, 6 insertions(+), 4 deletions(-) diff --git a/bezout.tex b/bezout.tex index 3b397e7..caa634a 100644 --- a/bezout.tex +++ b/bezout.tex @@ -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. -- cgit v1.2.3-54-g00ecf