Bold Diagrammatic Monte Carlo in the Lens of Stochastic Iterative Methods

TL;DR

This paper analyzes the convergence properties of bold diagrammatic Monte Carlo methods by framing them as stochastic iterative methods, providing insights into their efficiency and stability through theoretical and numerical analysis.

Contribution

It introduces a novel perspective by connecting BDMC with stochastic iterative methods, offering a deeper understanding of convergence enhancement techniques.

Findings

BDMC's convergence depends on condition number analysis.

Numerical experiments compare BDMC with related stochastic approaches.

Insights into stability and efficiency of BDMC methods.

Abstract

This work aims at understanding of bold diagrammatic Monte Carlo (BDMC) methods for stochastic summation of Feynman diagrams from the angle of stochastic iterative methods. The convergence enhancement trick of the BDMC is investigated from the analysis of condition number and convergence of the stochastic iterative methods. Numerical experiments are carried out for model systems to compare the BDMC with related stochastic iterative approaches.