Let $X:(\Omega,\Sigma)\rightarrow (\mathbb{R}^d;\mathbb{B}(\mathbb{R}^d))$ be a Borel-measurable random-vector.  What are some general classes of such-random vector for which one can give a "lower concentration inequality" of the form:
$$
\mathbb{P}(\|X\|>\lambda) \geq \mbox{"insert non-trivial lower-bound"}
$$
where $\lambda>0$.