From cd03b8d93912907348899b738511a4d0b5adf065 Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Thu, 10 Dec 2020 12:18:27 +0100 Subject: Added some bolded comments. --- bezout.tex | 2 ++ 1 file changed, 2 insertions(+) diff --git a/bezout.tex b/bezout.tex index 5b2a3c8..67544c4 100644 --- a/bezout.tex +++ b/bezout.tex @@ -286,6 +286,7 @@ the numerator of the Green function gives \right] \right\} \end{equation} + \textcolor{red}{\textbf{Not sure if the $N$ belongs here...}} with sums taken over repeated latin indices. The average can then be made over $J$ and Hubbard--Stratonovich used to change variables to replica matrices @@ -311,6 +312,7 @@ values follows from the jump across the cut, or \begin{equation} \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} +\textcolor{red}{\textbf{Missing a factor of two? Please check...}} The transition from a one-cut to two-cut singular value spectrum naturally corresponds to the origin leaving the support of the eigenvalue spectrum. -- cgit v1.2.3-70-g09d2