Statistical analysis method for the worldvolume hybrid Monte Carlo algorithm

Abstract We discuss the statistical analysis method for worldvolume hybrid Monte Carlo (WV-HMC) algorithm [M. Fukuma and N. Matsumoto, Prog. Theor. Exp. Phys. 2021, 023B08 (2021)], which was recently introduced to substantially reduce computational cost of tempered Lefschetz thimble method. In WV-HMC algorithm, configuration space is a continuous accumulation (worldvolume) deformed integration surfaces, sample averages are considered various subregions in worldvolume. prove that, if generated as Markov chain, then subsample subregion can also be regarded chain. This ensures application standard techniques algorithm. particularly investigate autocorrelation times chains subregions, find that there linear relation between probability being time corresponding subsample. numerically confirm this scaling law chiral random matrix model.