An integration by parts formula is derived for the first-order differential operator corresponding to the action of translations on the space of locally finite simple configurations of infinitely many points on d. As reference measures, tempered grand canonical Gibbs measures are considered corresponding to a non-constant non-smooth intensity (one-body potential) and translation invariant potentials fulfilling the usual conditions. It is proven that such Gibbs measures fulfill the intuitive integration by parts formula if and only if the action of the translation is not broken for this particular measure. The latter is automatically fulfilled in the high temperature and low intensity regime. © 2012 World Scientific Publishing Company.

A note on an integration by parts formula for the generators of uniform translations on configuration space

Kuna T.
2012

Abstract

An integration by parts formula is derived for the first-order differential operator corresponding to the action of translations on the space of locally finite simple configurations of infinitely many points on d. As reference measures, tempered grand canonical Gibbs measures are considered corresponding to a non-constant non-smooth intensity (one-body potential) and translation invariant potentials fulfilling the usual conditions. It is proven that such Gibbs measures fulfill the intuitive integration by parts formula if and only if the action of the translation is not broken for this particular measure. The latter is automatically fulfilled in the high temperature and low intensity regime. © 2012 World Scientific Publishing Company.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/175997
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