diff options
Diffstat (limited to 'frsb_kac-rice.tex')
| -rw-r--r-- | frsb_kac-rice.tex | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex index 2d2e003..c31cb62 100644 --- a/frsb_kac-rice.tex +++ b/frsb_kac-rice.tex @@ -50,7 +50,7 @@ when the actual ground-state of the model was computed by Parisi with a different scheme, the Bray--Moore result was not exact, and the problem has been open ever since \cite{Parisi_1979_Infinite}. To date, the program of computing the number of stationary points---minima, saddle points, and -maxima---of a mean-field glass has been only carried out for a small subset of +maxima---of mean-field complex landscapes has been only carried out for a small subset of models, including most notably the (pure) $p$-spin model ($p>2$) \cite{Rieger_1992_The, Crisanti_1995_Thouless-Anderson-Palmer} and for similar energy functions inspired by molecular biology, evolution, and machine learning @@ -1268,7 +1268,7 @@ exponentially many stationary points. A cartoon of this picture is shown in Fig. } \label{fig:cartoon} \end{figure} -\subsubsection{A concrete example} +\subsubsection{A tractable example} One can construct a schematic 2RSB model from two 1RSB models. Consider two independent pure models of size $N$ and with $p_1$-spin and $p_2$-spin couplings, @@ -1411,7 +1411,7 @@ saddles of random mean-field landscapes, including systems with many steps of RSB. For systems with full RSB, we find that minima are exponentially subdominant with respect to saddles at all energy densities above the ground state. The solution contains valuable geometric information that has yet to be -extracted in all detail. +extracted in all detail, for example considering several copies of the system \cite{cavagna1997structure}, or the extension to complex variables \cite{kent2021complex,kent2022analytic}. A first and very important application of the method here is to perform the calculation for high dimensional spheres, where it would give us a clear |