Gamma Expansions of Level Two Large Deviation Rate Functionals for Metastable Diffusions

Consider the diffusions $dX_t^\varepsilon=b(X_t^\varepsilon)dt+\sqrt{2\varepsilon}σ(X_t^\varepsilon)dB_t$ on $\mathbb{R}^d$, where $b$ and $σ$ are smooth coefficients and $B_t$ is an $r$-dimensional Brownian motion, with $r\le d$. We allow nonreversible dynamics and a degenerate diffusion matrix. Le