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  • Open Access

Ensemble averages, Poisson processes, and microstates

Cheng Peng*

  • Kavli Institute for Theoretical Sciences (KITS) and CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China and Center for Quantum Mathematics and Physics (QMAP), Department of Physics, University of California, Davis, California 95616, USA

  • *pengcheng@ucas.ac.cn
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Phys. Rev. D 103, L061901 – Published 22 March, 2021

DOI: https://doi.org/10.1103/PhysRevD.103.L061901

Abstract

Ensemble averages of random field theories have recently become promising candidates of the holographic dual of classical gravity. Since quantum theories are discrete, we initiate the study of consistent averages over theories with discrete random variables—which admit a mathematically rigorous description as Poisson processes—and get results that mirror Liouville gravity. We show that this is equivalent to averaging over an ensemble of states in a single microscopic theory, which is an early top-down example trying to answer the crucial question of whether the gravitational path integral computes an ensemble average over true randomness or over pseudorandomness coming from a large number of microstates.

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Phys. Rev. D 103, L061901– Published 22 March, 2021
  • Received 13 January 2021
  • Accepted 17 February 2021
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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