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 \( \langle (\mathbf{r}(t)-\mathbf{r}_{0})^{2}\rangle =6Dt \).