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authorJaron Kent-Dobias <jaron@kent-dobias.com>2022-06-07 18:23:01 +0200
committerJaron Kent-Dobias <jaron@kent-dobias.com>2022-06-07 18:23:01 +0200
commitdf9032a8c09f0c95e8a41c9825bc801e4310430f (patch)
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Fixed mistake in spetrum.
Diffstat (limited to 'frsb_kac_new.tex')
-rw-r--r--frsb_kac_new.tex2
1 files changed, 1 insertions, 1 deletions
diff --git a/frsb_kac_new.tex b/frsb_kac_new.tex
index 4932050..552ee9b 100644
--- a/frsb_kac_new.tex
+++ b/frsb_kac_new.tex
@@ -61,7 +61,7 @@ $\partial\partial H$ is a GOE matrix with variance
\end{equation}
and therefore its spectrum is given by the Wigner semicircle with radius $\sqrt{4f''(1)}$, or
\begin{equation}
- \rho(\lambda)=\frac1{\pi\sqrt{f''(1)}}\sqrt{\lambda^2-4f''(1)}
+ \rho(\lambda)=\frac1{\pi\sqrt{f''(1)}}\sqrt{4f''(1)-\lambda^2}
\end{equation}
and the spectrum of $\operatorname{Hess}H$ is this shifted by $\mu$, or $\rho(\lambda+\mu)$.