From 6b572dca1c4e53537352d9d4b09fccb637f392c9 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
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(-)

(limited to 'bezout.tex')

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

