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authorJaron Kent-Dobias <jaron@kent-dobias.com>2020-12-10 11:50:38 +0100
committerJaron Kent-Dobias <jaron@kent-dobias.com>2020-12-10 11:50:38 +0100
commitb8cf57637e7d11e7c1cb27b04f88ed2d5a04ee87 (patch)
treeb0841ba1c43ea15298b3f30273158802ada11d25
parenta1fb7e418d070fa4a3341cb0dc37e69c24f09b2b (diff)
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Added correct average to Green function.
-rw-r--r--bezout.tex2
1 files changed, 1 insertions, 1 deletions
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