Functional measures on the space of n-dimensional Riemannian geometries

Details Functional measures on the space of n-dimensional Riemannian geometries Functional measures on the space of n-dimensional Riemannian geometries

Mar 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989phrvl..62.1339c&link_type=abstract

Physical Review Letters, Volume 62, Issue 12, March 20, 1989, pp.1339-1342

Mathematics

Probability

4

Scientific paper

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.

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