  We consider Langevin dynamics associated with a modified kinetic energy
vanishing for small momenta. This allows us to freeze slow particles, and hence
avoid the re-computation of inter-particle forces, which leads to computational
gains. On the other hand, the statistical error may increase since there are a
priori more correlations in time. The aim of this work is first to prove the
ergodicity of the modified Langevin dynamics (which fails to be hypoelliptic),
and next to analyze how the asymptotic variance on ergodic averages depends on
the parameters of the modified kinetic energy. Numerical results illustrate the
approach, both for low-dimensional systems where we resort to a Galerkin
approximation of the generator, and for more realistic systems using Monte
Carlo simulations.
