A NOTE ON AN INTEGRATION BY PARTS FORMULA FOR THE GENERATORS OF UNIFORM TRANSLATIONS ON CONFIGURATION SPACE-Reference-Cited by-同舟云学术

A NOTE ON AN INTEGRATION BY PARTS FORMULA FOR THE GENERATORS OF UNIFORM TRANSLATIONS ON CONFIGURATION SPACE

Published:2012-12 Issue:04 Volume:15 Page:1250028
ISSN:0219-0257
Container-title:Infinite Dimensional Analysis, Quantum Probability and Related Topics
language:en
Short-container-title:Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

Author:

CONRAD FLORIAN¹²,KUNA TOBIAS³

Affiliation:

1. Department of Mathematics, University of Kaiserslautern, P. O. Box 3049, 67653 Kaiserslautern, Germany

2. Mathematics Department, Bielefeld University, P. O. Box 100131, 33501 Bielefeld, Germany

3. Department of Mathematics, The University of Reading, P. O. Box 220, Reading, Berkshire RG6 6AX, United Kingdom

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 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219025712500282

Reference6 articles.

1. Analysis and Geometry on Configuration Spaces: The Gibbsian Case

2. M. Z. Guo and G. Papanicolaou, Probabilistic Methods in Mathematical Physics (Academic Press, Inc., Boston, Mass., 1987) pp. 113–151.

3. HARMONIC ANALYSIS ON CONFIGURATION SPACE I: GENERAL THEORY

4. On the absence of phase transition in continuous one-dimensional Gibbs systems with no hard core

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