Let \((M,g)\) be a compact Riemannian surface without boundary. Consider the corresponding \(L^2\)-normalized Laplace-Beltrami eigenfunctions. In joint work in progress with Malabika Pramanik (U. British Columbia), I will present a result on the \(L^2\) restriction of these eigenfunctions to random Cantor-type sets. This, in some sense, is complementary to the smooth submanifold \(L^p\) restriction results of Burq-Gérard-Tzetkov ’06 (and later work of other authors). Our method includes concentration inequalities from probability theory.