Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-08-28
Russian Mathematical Surveys, 2001, v. 56, No. 5, 917
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
37 pages, 2 figures
Scientific paper
Gibbs measure is one of the central objects of the modern probability, mathematical statistical physics and euclidean quantum field theory. Here we define and study its natural generalization for the case when the space, where the random field is defined is itself random. Moreover, this randomness is not given apriori and independently of the configuration, but rather they depend on each other, and both are given by Gibbs procedure; We call the resulting object a Gibbs family because it parametrizes Gibbs fields on different graphs in the support of the distribution. We study also quantum (KMS) analog of Gibbs families. Various applications to discrete quantum gravity are given.
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