From b8cf57637e7d11e7c1cb27b04f88ed2d5a04ee87 Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Thu, 10 Dec 2020 11:50:38 +0100 Subject: Added correct average to Green function. --- bezout.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'bezout.tex') diff --git a/bezout.tex b/bezout.tex index a8f704c..92fcbf3 100644 --- a/bezout.tex +++ b/bezout.tex @@ -309,7 +309,7 @@ solution. A detailed analysis of the saddle point integration is needed to understand why this is so. Given such $\alpha_0$, the density of singular values follows from the jump across the cut, or \begin{equation} - \rho(\sigma)=\frac1{i\pi}\left(\lim_{\mathop{\mathrm{Im}}\sigma\to0^+}G(\sigma)-\lim_{\mathop{\mathrm{Im}}\sigma\to0^-}G(\sigma)\right) + \rho(\sigma)=\frac1{i\pi}\left(\lim_{\mathop{\mathrm{Im}}\sigma\to0^+}\overline G(\sigma)-\lim_{\mathop{\mathrm{Im}}\sigma\to0^-}\overline G(\sigma)\right) \end{equation} The transition from a one-cut to two-cut singular value spectrum naturally -- cgit v1.2.3-54-g00ecf