From df9032a8c09f0c95e8a41c9825bc801e4310430f Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Tue, 7 Jun 2022 18:23:01 +0200 Subject: Fixed mistake in spetrum. --- frsb_kac_new.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'frsb_kac_new.tex') 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 $\rho(\lambda+\mu)$. -- cgit v1.2.3-70-g09d2