Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 164, Issue 4, Pages 735-771Publisher
SPRINGER
DOI: 10.1007/s10955-016-1544-6
Keywords
Langevin dynamics; Variance reduction; Ergodicity; Functional estimates; Linear response
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Funding
- European Research Council through ERC [307629]
- Agence Nationale de la Recherche [ANR-14-CE23-0012]
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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.
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