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: $$ \mathbb{P}(\|X\|^2>\lambda) \geq \mbox{(insert non-trivial lower bound)} $$ where $\lambda>0$.