We consider $g(X)$ where $X = (\varepsilon_{ij})_{1 \leqslant i \leqslant k, 1 \leqslant j \leqslant d}$ is a random variable with independent Rademacher coefficients and $g(M) = \|M \cdot u\|$ for a fixed unit vector $u$. Deduce from the above that, for every strictly positive real number $t$
$$\mathbb{P}(|g(X) - m| \geqslant t) \leqslant 4\exp\left(-\frac{1}{8}t^{2}\right)$$
where $m$ is a median of $g(X)$.