Asymptotics of Fixed Point Distributions for Inexact Monte Carlo Algorithms

Abstract

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.

24 pages, accepted for publication in Physics Review D

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Cited by in corpus (6)

• Shadow Hamiltonians, Poisson Brackets, and Gauge Theories
• Improving dynamical lattice QCD simulations through integrator tuning using Poisson brackets and a force-gradient integrator
• Topological tunneling with Dynamical overlap fermions
• Investigation of New Methods for Numerical Stochastic Perturbation Theory in ${\phi }^4$ Theory
• Force Gradient Integrators
• Tuning the Hybrid Monte Carlo algorithm using molecular dynamics forces' variances