Phys. Rev. Lett. 62, 1339–1342 (1989)Functional measures on the space of n-dimensional Riemannian geometriesReceived 13 June 1988; published in the issue dated 20 March 1989 By exploiting some recent results in global Riemannian geometry we construct families of probability measures on the path space associated with the set of n-dimensional (n≥3) Riemannian geometries. As an example of such construction we characterize a Gaussian stochastic process which yields a natural notion of Brownian motion on the set of Riemannian manifolds. An ultraviolet cutoff L parametrizes this class of measures. The limit L→0, as well as the probability of finding a random geometry in a given state, is discussed. © 1989 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.62.1339
DOI:
10.1103/PhysRevLett.62.1339
PACS:
04.60.+n, 02.30.+g
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