= Solution
In the low-temperature regime, the particle rapidly equilibrates near a minimum and only rarely crosses a neighboring maximum. Applying <Laplace's method> to the exact current formula gives the <Kramers escape rates>
$$
k_+=\frac{\sqrt{|\phi''(m_0)\phi''(M_1)|}}{2\pi}e^{-\Delta\phi_+/D},
\qquad
k_-=\frac{\sqrt{|\phi''(m_0)\phi''(M_0)|}}{2\pi}e^{-\Delta\phi_-/D}.
$$
Each right or left escape changes position by $2\pi$, hence
$$
\boxed{v_s\simeq2\pi(k_+-k_-).}
$$
The reduced <continuous-time random walk> on minima has off-diagonal transition rates
$$
\boxed{W(k|l)=k_+\delta_{k,l+1}+k_-\delta_{k,l-1},}
$$
and diagonal generator entry $W(l|l)=-(k_++k_-)$. Its residence time in each well is exponentially distributed with rate $k_++k_-$, and the next jump is right with probability $k_+/(k_++k_-)$.
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