  We prove a quantitative version of the Faber-Krahn inequality for the first
eigenvalue of the fractional Dirichlet-Laplacian of order s. This is done by
using the so-called Caffarelli-Silvestre extension and adapting to the nonlocal
setting a trick by Hansen and Nadirashvili. The relevant stability estimate
comes with an explicit constant, which is stable as the fractional order of
differentiability goes to 1.
