Palm pairs and the general mass-transport principle |
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Authors: | Daniel Gentner G��nter Last |
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Affiliation: | 1. Institut f??r Stochastik, Universit?t Karlsruhe (TH), 76128, Karlsruhe, Germany
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Abstract: | We consider a lcsc group G acting on a Borel space S and on an underlying ??-finite measure space. Our first main result is a transport formula connecting the Palm pairs of jointly stationary random measures on S. A key (and new) technical result is a measurable disintegration of the Haar measure on G along the orbits. The second main result is an intrinsic characterization of the Palm pairs of a G-invariant random measure. We then proceed with deriving a general version of the mass-transport principle for possibly non-transitive and non-unimodular group operations first in a deterministic and then in its full probabilistic form. |
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