  Because all stars contribute to its gravitational potential, stellar clusters
amplify perturbations collectively. In the limit of small fluctuations, this is
described through linear response theory, via the so-called response matrix.
While the evaluation of this matrix is somewhat straightforward for unstable
modes (i.e. with a positive growth rate), it requires a careful analytic
continuation for damped modes (i.e. with a negative growth rate). We present a
generic method to perform such a calculation in spherically symmetric stellar
clusters. When applied to an isotropic isochrone cluster, we recover the
presence of a low-frequency weakly damped $\ell = 1$ mode. We finally use a set
of direct $N$-body simulations to test explicitly this prediction through the
statistics of the correlated random walk undergone by a cluster's density
centre.
