  The paper is devoted to studying the stability of random sampling in a
localized reproducing kernel space. We show that if the sampling set on
$\Omega$ (compact) discretizes the integral norm of simple functions up to a
given error, then the sampling set is stable for the set of functions
concentrated on $\Omega$. Moreover, we prove with an overwhelming probability
that ${\mathcal O}(\mu(\Omega)(\log \mu(\Omega))^3)$ many random points
uniformly distributed over $\Omega$ yield a stable set of sampling for
functions concentrated on $\Omega$.
