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

Conrad, F. and Kuna, T. (2012) A note on an integration by parts formula for the generators of uniform translations on configuration space. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 15 (4). 1250028. ISSN 0219-0257

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To link to this item DOI: 10.1142/S0219025712500282

Abstract/Summary

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 Rd. 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.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:29252
Publisher:World Scientific Publishing

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