Stochastic sum and the probability of large deviations for time (Q2746885)

5-dimensional space-time is considered with foliation of codimension 1. The author constructs fluctuations of the metric of the foliation such that their contribution to the Feynmann path integral over 5-dimensional trajectories is the same as the contribution of the real physical space-time. She also constructs the statistical sum \(Z\) of the canonical ensemble of 5-metrics determined by a parameter and uses \(Z\) to calculate the probability of the metric with a given parameter. An analogue of the Einstein formula is used to evaluate the probability of the metric fluctuations.