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| -rw-r--r-- | bezout.tex | 6 |
1 files changed, 2 insertions, 4 deletions
@@ -100,9 +100,7 @@ shift, or $\rho(\lambda)=\rho_0(\lambda+p\epsilon)$. The Hessian of \partial_i\partial_jH_0 =\frac{p(p-1)}{p!}\sum_{k_1\cdots k_{p-2}}^NJ_{ijk_1\cdots k_{p-2}}z_{k_1}\cdots z_{k_{p-2}}, \end{equation} -which makes its ensemble that of Gaussian complex symmetric matrices, whose -spectrum is constant inside the support of a certain ellipse and zero -everywhere else \cite{Nguyen_2014_The}. Given its variances +which makes its ensemble that of Gaussian complex symmetric matrices. Given its variances $\langle|\partial_i\partial_j H_0|^2\rangle=p(p-1)a^{p-2}/2N$ 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} @@ -110,7 +108,7 @@ $\langle(\partial_i\partial_j H_0)^2\rangle=p(p-1)\kappa/2N$, $\rho_0(\lambda)$ \left(\frac{\mathop{\mathrm{Im}}(\lambda e^{i\theta})}{1-|\kappa|/a^{p-2}}\right)^2 <\frac12p(p-1)a^{p-2} \end{equation} -where $\theta=\frac12\arg\kappa$. +where $\theta=\frac12\arg\kappa$ \cite{Nguyen_2014_The}. \bibliographystyle{apsrev4-2} \bibliography{bezout} |