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| -rw-r--r-- | bezout.tex | 6 |
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@@ -111,9 +111,9 @@ which makes its ensemble that of Gaussian complex symmetric matrices. Given its $\langle|\partial_i\partial_j H_0|^2\rangle=p(p-1)a^{p-2}/2N$ and $\langle(\partial_i\partial_j H_0)^2\rangle=p(p-1)\kappa/2N$, $\rho_0(\lambda)$ is constant inside the ellipse \begin{equation} \label{eq:ellipse} - \left(\frac{\mathop{\mathrm{Re}}(\lambda e^{i\theta})}{1+|\kappa|/a^{p-2}}\right)^2+ - \left(\frac{\mathop{\mathrm{Im}}(\lambda e^{i\theta})}{1-|\kappa|/a^{p-2}}\right)^2 - <\frac12p(p-1)a^{p-2} + \left(\frac{\mathop{\mathrm{Re}}(\lambda e^{i\theta})}{a^{p-2}+|\kappa|}\right)^2+ + \left(\frac{\mathop{\mathrm{Im}}(\lambda e^{i\theta})}{a^{p-2}-|\kappa|}\right)^2 + <\frac{p(p-1)}{2a^{p-2}} \end{equation} where $\theta=\frac12\arg\kappa$ \cite{Nguyen_2014_The}. |