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author | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2022-06-07 18:23:01 +0200 |
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committer | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2022-06-07 18:23:01 +0200 |
commit | df9032a8c09f0c95e8a41c9825bc801e4310430f (patch) | |
tree | a313c2b1dbab9415928fc777a0a05658e2d65e1f | |
parent | 9dba5cf192045a0549af907fcc9e664932ce1fee (diff) | |
download | PRE_107_064111-df9032a8c09f0c95e8a41c9825bc801e4310430f.tar.gz PRE_107_064111-df9032a8c09f0c95e8a41c9825bc801e4310430f.tar.bz2 PRE_107_064111-df9032a8c09f0c95e8a41c9825bc801e4310430f.zip |
Fixed mistake in spetrum.
-rw-r--r-- | frsb_kac_new.tex | 2 |
1 files changed, 1 insertions, 1 deletions
diff --git a/frsb_kac_new.tex b/frsb_kac_new.tex index 4932050..552ee9b 100644 --- a/frsb_kac_new.tex +++ b/frsb_kac_new.tex @@ -61,7 +61,7 @@ $\partial\partial H$ is a GOE matrix with variance \end{equation} and therefore its spectrum is given by the Wigner semicircle with radius $\sqrt{4f''(1)}$, or \begin{equation} - \rho(\lambda)=\frac1{\pi\sqrt{f''(1)}}\sqrt{\lambda^2-4f''(1)} + \rho(\lambda)=\frac1{\pi\sqrt{f''(1)}}\sqrt{4f''(1)-\lambda^2} \end{equation} and the spectrum of $\operatorname{Hess}H$ is this shifted by $\mu$, or $\rho(\lambda+\mu)$. |