Past exam of the random matrix theory course of the University of Oxford / 2025 / 3 / b / i

Apply the same characteristic polynomial calculation with $U$ replaced by $B(t)$. Pathwise,The real-valued processes $\pm B(t)$ give continuous lifts of these angles. The eigenvalues coincide whenever $B(t)\in \pi \mathbb{Z}$; the exponential formulas remain valid at those times.