Error Analysis of Modified Langevin Dynamics

Stephane Redon 1 Gabriel Stoltz 2, 3 Zofia Trstanova 1
1 NANO-D - Algorithms for Modeling and Simulation of Nanosystems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique, Inria de Paris
Abstract : 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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Submitted on : Thursday, January 28, 2016 - 10:21:51 AM
Last modification on : Thursday, April 26, 2018 - 10:28:55 AM

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Stephane Redon, Gabriel Stoltz, Zofia Trstanova. Error Analysis of Modified Langevin Dynamics. Journal of Statistical Physics, Springer Verlag, 2016, 164 (4), pp.735-771. ⟨10.1007/s10955-016-1544-6⟩. ⟨hal-01263700⟩



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