Journal of High Energy Physics

, 2018:60 | Cite as

Emergence of AdS geometry in the simulated tempering algorithm

  • Masafumi Fukuma
  • Nobuyuki MatsumotoEmail author
  • Naoya Umeda
Open Access
Regular Article - Theoretical Physics


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 global geometry of a stochastic system whose equilibrium distribution is highly multimodal with a large number of degenerate vacua. We show that, when the simulated tempering algorithm is implemented to such a system, the extended configuration space has an asymptotically Euclidean anti-de Sitter (AdS) geometry. We further show that this knowledge of geometry enables us to optimize the tempering parameter in a simple, geometrical way.


Random Systems Stochastic Processes Lattice QCD AdS-CFT Correspondence 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Masafumi Fukuma
    • 1
  • Nobuyuki Matsumoto
    • 1
    Email author
  • Naoya Umeda
    • 2
  1. 1.Department of PhysicsKyoto UniversityKyotoJapan
  2. 2.PricewaterhouseCoopers Aarata LLCTokyoJapan

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