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-rw-r--r--bezout.tex40
-rw-r--r--fig/spectra_0.0.pdfbin0 -> 23571 bytes
-rw-r--r--fig/spectra_0.5.pdfbin0 -> 23917 bytes
-rw-r--r--fig/spectra_1.0.pdfbin0 -> 24516 bytes
-rw-r--r--fig/spectra_1.5.pdfbin0 -> 24327 bytes
-rw-r--r--fig/spectra_eigenvalue_0.0.pdfbin6861 -> 0 bytes
-rw-r--r--fig/spectra_eigenvalue_0.5.pdfbin6865 -> 0 bytes
-rw-r--r--fig/spectra_eigenvalue_1.0.pdfbin6859 -> 0 bytes
-rw-r--r--fig/spectra_eigenvalue_1.5.pdfbin6865 -> 0 bytes
-rw-r--r--fig/spectra_singular_0.0.pdfbin9319 -> 0 bytes
-rw-r--r--fig/spectra_singular_0.5.pdfbin9871 -> 0 bytes
-rw-r--r--fig/spectra_singular_1.0.pdfbin10376 -> 0 bytes
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13 files changed, 13 insertions, 27 deletions
diff --git a/bezout.tex b/bezout.tex
index a55b4bd..81e4718 100644
--- a/bezout.tex
+++ b/bezout.tex
@@ -220,36 +220,22 @@ is shifted by $p\epsilon$.
\begin{figure}[htpb]
\centering
- \raisebox{60pt}{$|\epsilon|=0$}
- \hfill
- \raisebox{5pt}{\includegraphics[scale=1.0]{fig/spectra_eigenvalue_0.0.pdf}}
- \hspace{2pt}
- \includegraphics{fig/spectra_singular_0.0.pdf}\\
- \raisebox{60pt}{$|\epsilon|=\frac12|\epsilon_{\mathrm{th}}|$}
- \hfill
- \raisebox{5pt}{\includegraphics[scale=1.0]{fig/spectra_eigenvalue_0.5.pdf}}
- \hspace{2pt}
- \includegraphics{fig/spectra_singular_0.5.pdf}\\
- \raisebox{60pt}{$|\epsilon|=|\epsilon_{\mathrm{th}}|$}
- \hfill
- \raisebox{5pt}{\includegraphics[scale=1.0]{fig/spectra_eigenvalue_1.0.pdf}}
- \hspace{2pt}
- \includegraphics{fig/spectra_singular_1.0.pdf}\\
- \raisebox{60pt}{$|\epsilon|=\frac32|\epsilon_{\mathrm{th}}|$}
- \hfill
- \raisebox{5pt}{\includegraphics[scale=1.0]{fig/spectra_eigenvalue_1.5.pdf}}
- \hspace{2pt}
- \includegraphics{fig/spectra_singular_1.5.pdf}
+ \includegraphics{fig/spectra_0.0.pdf}
+ \includegraphics{fig/spectra_0.5.pdf}\\
+ \includegraphics{fig/spectra_1.0.pdf}
+ \includegraphics{fig/spectra_1.5.pdf}
\caption{
Eigenvalue and singular value spectra of the matrix $\partial\partial H$
- for $p=3$, $a=\frac54$, $\kappa=\frac34e^{i3\pi/4}$, and
- $\epsilon=i|\epsilon|$ with various values of $|\epsilon|$. The shaded
- region of the lefthand plots shows the support of the eigenvalue
- distribution. The solid line on the righthand plots shows the distribution
- of singular values, while the overlaid histograms show empirical
- distributions from $2^{10}\times2^{10}$ complex normal matrices with the
- same covariance and diagonal shift as $\partial\partial H$.
+ for $p=3$, $a=\frac54$, and $\kappa=\frac34e^{i3\pi/4}$ with (a)
+ $\epsilon=0$, (b) $\epsilon=\frac12|\epsilon_{\mathrm{th}}|$, (c)
+ $\epsilon=|\epsilon_{\mathrm{th}}|$, and (d)
+ $\epsilon=\frac32|\epsilon_{\mathrm{th}}|$. The shaded region of each inset
+ shows the support of the eigenvalue distribution. The solid line on each
+ plot shows the distribution of singular values, while the overlaid
+ histogram shows the empirical distribution from $2^{10}\times2^{10}$ complex
+ normal matrices with the same covariance and diagonal shift as
+ $\partial\partial H$.
} \label{fig:spectra}
\end{figure}
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