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| author | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2022-06-04 18:25:27 +0200 |
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| committer | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2022-06-04 18:25:27 +0200 |
| commit | 76744598b778dd585ed6bf2486f6075dfd6112d5 (patch) | |
| tree | e4c81504f25946593649ddc371943d873b3d0a2a | |
| parent | cfbe1940131089ef25e72dc69948c379ab6ae0ee (diff) | |
| download | PRE_107_064111-76744598b778dd585ed6bf2486f6075dfd6112d5.tar.gz PRE_107_064111-76744598b778dd585ed6bf2486f6075dfd6112d5.tar.bz2 PRE_107_064111-76744598b778dd585ed6bf2486f6075dfd6112d5.zip | |
Some changes.
| -rw-r--r-- | frsb_kac-rice.tex | 8 |
1 files changed, 3 insertions, 5 deletions
diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex index 3f5854c..87445c7 100644 --- a/frsb_kac-rice.tex +++ b/frsb_kac-rice.tex @@ -258,12 +258,10 @@ Taking the saddle with respect to $\mu$ and $F_d$ yields and gives \begin{align*} \Sigma - =-\epsilon\hat\epsilon+\lim_{n\to0}\frac1n\frac12\left( - n - \hat\epsilon R_df'(1) - +\hat\epsilon^2\sum_{ab} + =\epsilon\hat\epsilon+\hat\epsilon R_d f'(1)+\frac12D_df'(1)+\lim_{n\to0}\frac1n\frac12\left( + \hat\epsilon^2\sum_{ab} f(Q_{ab}) - +\log\det(\hat\epsilon R_d^{-1} Q+I) + +\log\det(-D_dR_d^{-2} Q+I) \right) \end{align*} Finally, setting $0=\Sigma$ gives |