Emergence of AdS geometry in the simulated tempering algorithm
Abstract
In our previous work [1], we introduced to an arbitrary Markov chain Monte Carlo algorithm a distance between configurations. This measures the difficulty of transition from one configuration to the other, and enables us to investigate the relaxation of probability distribution from a geometrical point of view. In this paper, we investigate the geometry of stochastic systems whose equilibrium distributions are highly multimodal with a large number of degenerate vacua. Implementing the simulated tempering algorithm to such a system, we show that an asymptotically Euclidean anti-de Sitter geometry emerges with a horizon in the extended configuration space when the tempering parameter is optimized such that distances get minimized.
Cite
@article{arxiv.1806.10915,
title = {Emergence of AdS geometry in the simulated tempering algorithm},
author = {Masafumi Fukuma and Nobuyuki Matsumoto and Naoya Umeda},
journal= {arXiv preprint arXiv:1806.10915},
year = {2018}
}
Comments
19 pages, 5 figures. v2: typos corrected, some discussions improved