Asymptotics of Fixed Point Distributions for Inexact Monte Carlo Algorithms

Details Asymptotics of Fixed Point Distributions for Inexact Monte Carlo Algorithms Asymptotics of Fixed Point Distributions for Inexact Monte Carlo Algorithms

2007-05-14

arxiv.org/abs/0705.2014v3

Phys.Rev.D76:074508,2007

Physics

High Energy Physics

High Energy Physics - Lattice

24 pages, accepted for publication in Physics Review D

Scientific paper

10.1103/PhysRevD.76.074508

We introduce a simple general method for finding the equilibrium distribution for a class of widely used inexact Markov Chain Monte Carlo algorithms. The explicit error due to the non-commutivity of the updating operators when numerically integrating Hamilton's equations can be derived using the Baker-Campbell-Hausdorff formula. This error is manifest in the conservation of a ``shadow'' Hamiltonian that lies close to the desired Hamiltonian. The fixed point distribution of inexact Hybrid algorithms may then be derived taking into account that the fixed point of the momentum heatbath and that of the molecular dynamics do not coincide exactly. We perform this derivation for various inexact algorithms used for lattice QCD calculations.

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