Uniqueness of the minimizer for a random nonlocal functional with double-well potential in $d\le 2$

Nicolas Dir, Enza Orlandi

We consider a small random perturbation of the energy functional $$[u{]}_{H^s(\Lambda ,R^d)}^2+{\int }_{\Lambda }W(u(x))dx$$ for $s\in (0,1),$ where the non-local part $[u{]}_{H^s(\Lambda ,R^d)}^2$ deno…