  This paper is devoted to stability estimates for the interaction energy with
strictly radially decreasing interaction potentials, such as the Coulomb and
Riesz potentials. For a general density function, we first prove a stability
estimate in terms of the $L^1$ asymmetry of the density, extending some
previous results by Burchard-Chambers, Frank-Lieb and Fusco-Pratelli for
characteristic functions. We also obtain a stability estimate in terms of the
2-Wasserstein distance between the density and its radial decreasing
rearrangement. Finally, we consider the special case of Newtonian potential,
and address a conjecture by Guo on the stability for the Coulomb energy.
