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
Ω (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 Ω. Moreover, we prove with an overwhelming probability
that O(μ(Ω)(logμ(Ω))3) many random points
uniformly distributed over Ω yield a stable set of sampling for
functions concentrated on Ω.Comment: 17 page