Equation 12.4.2E544AEC2FDDB

\begin{align} \frac{\ddot\lambda }{\lambda } & =-\frac1n\int _ X \left\| A_\chi -\frac{\dot\lambda }{\lambda }I\right\| _\Omega ^2 \, \mathrm{d}\nu _\Omega ,\\ -\frac{\mathrm{d}^2}{\mathrm{d}t^2}\log \lambda _\mu (\theta _ t) & =\frac1n\int _ X\operatorname {tr}(A_\chi ^2)\, \mathrm{d}\nu _\Omega . \tag{12.4.3} \end{align}