Majority dynamics on finite trees

For an arbitrary finite tree $T$, we find the exact value of the wort-case stabilisation time of majority dynamics on $T$. We also prove that for a perfect rooted cubic tree $T$ with diameter $D$ and uniformly random initial opinions, the dynamics stabilises in time $\tau \in (D\mathrm{/}4,D\mathrm{/}3)$ with high probability.