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arXiv · 2107.06858

Statistical analysis method for the worldvolume hybrid Monte Carlo algorithm

Masafumi Fukuma·Nobuyuki Matsumoto·Yusuke Namekawa
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Abstract

We discuss the statistical analysis method for the worldvolume hybrid Monte Carlo (WV-HMC) algorithm [arXiv:2012.08468], which was recently introduced to substantially reduce the computational cost of the tempered Lefschetz thimble method. In the WV-HMC algorithm, the configuration space is a continuous accumulation (worldvolume) of deformed integration surfaces, and sample averages are considered for various subregions in the worldvolume. We prove that, if a sample in the worldvolume is generated as a Markov chain, then the subsample in the subregion can also be regarded as a Markov chain. This ensures the application of the standard statistical techniques to the WV-HMC algorithm. We particularly investigate the autocorrelation times for the Markov chains in various subregions, and find that there is a linear relation between the probability to be in a subregion and the autocorrelation time for the corresponding subsample. We numerically confirm this scaling law for a chiral random matrix model.

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Masafumi Fukuma, Nobuyuki Matsumoto, Yusuke Namekawa. 2021-07-14. Statistical analysis method for the worldvolume hybrid Monte Carlo algorithm. https://arxiv.org/abs/2107.06858

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