Ensemble averages, Poisson processes, and microstates

摘要

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.