For very large $t$ this becomes

$$\langle (\mathbf{r}(t)-\mathbf{r}_{0})^{2}\rangle =\frac{6kT}{m\xi }t$$

from which we get the Einstein relation

$$D= \frac{kT}{m\xi }$$

where we have used $\langle (\mathbf{r}(t)-\mathbf{r}_{0})^{2}\rangle =6Dt$.