Rapoport's dimension conjecture for affine Deligne–Lusztig varieties

Let $G$ be a connected reductive group over $F$, let $b\in G(L)$, and let $\mu$ be a dominant coweight such that the affine Deligne–Lusztig variety $X_\mu(b)$ is non-empty. Write $\bar\nu_b$ for the dominant Newton point of $b$, let $\rho$ be the half-sum of the positive roots, and let $\operatorname{def}_G(b)$ be the $F$-rank of $G$ minus the $F$-rank of the inner form $J$ of the centralizer group $M_b$. Rapoport's conjecture. The dimension of $X_\mu(b)$ is

$$\dim X_\mu(b)=\langle\rho,\mu-\bar\nu_b\rangle-\frac{1}{2}\operatorname{def}_G(b).$$

This is the expected dimension formula for non-empty affine Deligne–Lusztig varieties in the affine Grassmannian. The source presents it as conjectural and gives no resolution status.