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arXiv · 1806.10915

Emergence of AdS geometry in the simulated tempering algorithm

Masafumi Fukuma·Nobuyuki Matsumoto·Naoya Umeda
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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.

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Masafumi Fukuma, Nobuyuki Matsumoto, Naoya Umeda. 2018-08-14. Emergence of AdS geometry in the simulated tempering algorithm. https://doi.org/10.1007/jhep11(2018)060

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