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@@ -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} diff --git a/fig/spectra_0.0.pdf b/fig/spectra_0.0.pdf Binary files differnew file mode 100644 index 0000000..5d519e4 --- /dev/null +++ b/fig/spectra_0.0.pdf diff --git a/fig/spectra_0.5.pdf b/fig/spectra_0.5.pdf Binary files differnew file mode 100644 index 0000000..d58dc05 --- /dev/null +++ b/fig/spectra_0.5.pdf diff --git a/fig/spectra_1.0.pdf b/fig/spectra_1.0.pdf Binary files differnew file mode 100644 index 0000000..cfe372c --- /dev/null +++ b/fig/spectra_1.0.pdf diff --git a/fig/spectra_1.5.pdf b/fig/spectra_1.5.pdf Binary files differnew file mode 100644 index 0000000..92223f4 --- /dev/null +++ b/fig/spectra_1.5.pdf diff --git a/fig/spectra_eigenvalue_0.0.pdf b/fig/spectra_eigenvalue_0.0.pdf Binary files differdeleted file mode 100644 index 6b9b83e..0000000 --- a/fig/spectra_eigenvalue_0.0.pdf +++ /dev/null diff --git a/fig/spectra_eigenvalue_0.5.pdf b/fig/spectra_eigenvalue_0.5.pdf Binary files differdeleted file mode 100644 index 63104d6..0000000 --- a/fig/spectra_eigenvalue_0.5.pdf +++ /dev/null diff --git a/fig/spectra_eigenvalue_1.0.pdf b/fig/spectra_eigenvalue_1.0.pdf Binary files differdeleted file mode 100644 index 6e3ebe1..0000000 --- a/fig/spectra_eigenvalue_1.0.pdf +++ /dev/null diff --git a/fig/spectra_eigenvalue_1.5.pdf b/fig/spectra_eigenvalue_1.5.pdf Binary files differdeleted file mode 100644 index b68706e..0000000 --- a/fig/spectra_eigenvalue_1.5.pdf +++ /dev/null diff --git a/fig/spectra_singular_0.0.pdf b/fig/spectra_singular_0.0.pdf Binary files differdeleted file mode 100644 index 86c945d..0000000 --- a/fig/spectra_singular_0.0.pdf +++ /dev/null diff --git a/fig/spectra_singular_0.5.pdf b/fig/spectra_singular_0.5.pdf Binary files differdeleted file mode 100644 index b25caa0..0000000 --- a/fig/spectra_singular_0.5.pdf +++ /dev/null diff --git a/fig/spectra_singular_1.0.pdf b/fig/spectra_singular_1.0.pdf Binary files differdeleted file mode 100644 index 4cae0c1..0000000 --- a/fig/spectra_singular_1.0.pdf +++ /dev/null diff --git a/fig/spectra_singular_1.5.pdf b/fig/spectra_singular_1.5.pdf Binary files differdeleted file mode 100644 index e6f43fd..0000000 --- a/fig/spectra_singular_1.5.pdf +++ /dev/null |