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author | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2022-07-13 13:18:32 +0200 |
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committer | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2022-07-13 13:18:32 +0200 |
commit | 4f03a48fc19933764b67a59a0e48547d8720e9ec (patch) | |
tree | 397fe449a426993dbca763a53d13fa5bda131e52 /frsb_kac-rice.tex | |
parent | 6dee128a8f1bbf51814575bdbd11cc1ed6d6ac5e (diff) | |
download | PRE_107_064111-4f03a48fc19933764b67a59a0e48547d8720e9ec.tar.gz PRE_107_064111-4f03a48fc19933764b67a59a0e48547d8720e9ec.tar.bz2 PRE_107_064111-4f03a48fc19933764b67a59a0e48547d8720e9ec.zip |
Tiny disclaimer.
Diffstat (limited to 'frsb_kac-rice.tex')
-rw-r--r-- | frsb_kac-rice.tex | 11 |
1 files changed, 6 insertions, 5 deletions
diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex index ec3a933..10552b6 100644 --- a/frsb_kac-rice.tex +++ b/frsb_kac-rice.tex @@ -536,11 +536,12 @@ matrix products and Hadamard products. In particular, the determinant of the blo \begin{equation} \ln\det\begin{bmatrix}C&iR\\iR&D\end{bmatrix}=\ln\det(CD+R^2) \end{equation} -This is straightforward to write down at $k$RSB, since the product and sum of -the hierarchical matrices is still a hierarchical matrix. The algebra of -hierarchical matrices is reviewed in \S\ref{sec:dict}. Using the product formula -\eqref{eq:replica.prod}, one can write down the hierarchical matrix $CD+R^2$, -and then compute the $\ln\det$ using the formula \eqref{eq:replica.logdet}. +This is straightforward (if strenous) to write down at $k$RSB, since the +product and sum of the hierarchical matrices is still a hierarchical matrix. +The algebra of hierarchical matrices is reviewed in \S\ref{sec:dict}. Using the +product formula \eqref{eq:replica.prod}, one can write down the hierarchical +matrix $CD+R^2$, and then compute the $\ln\det$ using the formula +\eqref{eq:replica.logdet}. The extremal conditions are given by differentiating the complexity with respect to its parameters, yielding |