Error analysis of the transport properties of Metropolized schemes

2014/02/26 by Max Fathi, Fathi, Max, Ahmed-Amine Homman +3
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Numerical Analysis (math.NA) #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1402.6537

openalex publication_date 2014/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider in this work the numerical computation of transport coefficients for Brownian dynamics. We investigate the discretization error arising when simulating the dynamics with the Smart MC algorithm (also known as Metropolis-adjusted Langevin algorithm). We prove that the error is of order one in the time step, when using either the Green-Kubo or the Einstein formula to estimate the transport coefficients. We illustrate our results with numerical simulations.

Citations

• Monte Carlo sampling methods using Markov chains and their applications

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