From 1f2b3de07c9a8b39e32f621b07ee5e19895e46b9 Mon Sep 17 00:00:00 2001 From: "kurchan.jorge" Date: Mon, 7 Dec 2020 16:00:36 +0000 Subject: Update on Overleaf. --- bezout.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'bezout.tex') diff --git a/bezout.tex b/bezout.tex index 81fe628..573fe90 100644 --- a/bezout.tex +++ b/bezout.tex @@ -96,7 +96,7 @@ $N \Sigma= \overline{\ln \mathcal N_J} = \int dJ \; \ln N_J$, a calculation that involves the replica trick. In most, but not all, of the parameter-space that we shall study here, the {\em annealed approximation} $N \Sigma \sim \ln \overline{ \mathcal N_J} = \ln \int dJ \; N_J$ is exact. -A useful propert +A useful property } -- cgit v1.2.3-54-g00ecf From 075968fa95bd2ba34f14e52b0671ae558cd45ce9 Mon Sep 17 00:00:00 2001 From: "kurchan.jorge" Date: Mon, 7 Dec 2020 16:02:07 +0000 Subject: Update on Overleaf. --- bezout.tex | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) (limited to 'bezout.tex') diff --git a/bezout.tex b/bezout.tex index 573fe90..a29cd4b 100644 --- a/bezout.tex +++ b/bezout.tex @@ -96,7 +96,8 @@ $N \Sigma= \overline{\ln \mathcal N_J} = \int dJ \; \ln N_J$, a calculation that involves the replica trick. In most, but not all, of the parameter-space that we shall study here, the {\em annealed approximation} $N \Sigma \sim \ln \overline{ \mathcal N_J} = \ln \int dJ \; N_J$ is exact. -A useful property +A useful property of the Gaussian distributions is that gradient and Hessian may be seen to be independent \cite{BrayDean,Fyodorov}, +so that we may treat the delta-functions and the hessians as independent } -- cgit v1.2.3-54-g00ecf