We set $A_{k} = \frac{X}{\sqrt{k}}$ where $X = (\varepsilon_{ij})_{1 \leqslant i \leqslant k, 1 \leqslant j \leqslant d}$ is a random variable with independent Rademacher coefficients. Let $\varepsilon$ be in $]0, 1[$ and $\delta$ be in $]0, 1/2[$. We assume that $k \geqslant 160\frac{\ln(1/\delta)}{\varepsilon^{2}}$. Show that, for every unit vector $u$ in $\mathbb{R}^{d}$:
$$\mathbb{P}\left(\left|\|A_{k} \cdot u\| - 1\right| > \varepsilon\right) < \delta$$