Summability of Connected Correlation Functions of Coupled Lattice Fields

Show full item record



Permalink

http://hdl.handle.net/10138/300001

Citation

Lukkarinen , J , Marcozzi , M & Nota , A 2018 , ' Summability of Connected Correlation Functions of Coupled Lattice Fields ' , Journal of Statistical Physics , vol. 171 , no. 2 , pp. 189-206 . https://doi.org/10.1007/s10955-018-2000-6

Title: Summability of Connected Correlation Functions of Coupled Lattice Fields
Author: Lukkarinen, Jani; Marcozzi, Matteo; Nota, Alessia
Contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, University of Geneva
University of Helsinki, University of Bonn
Date: 2018-04
Language: eng
Number of pages: 18
Belongs to series: Journal of Statistical Physics
ISSN: 0022-4715
URI: http://hdl.handle.net/10138/300001
Abstract: We consider two nonindependent random fields and defined on a countable set Z. For instance, or , where I denotes a finite set of possible "internal degrees of freedom" such as spin. We prove that, if the cumulants of and enjoy a certain decay property, then all joint cumulants between and are -summable in the precise sense described in the text. The decay assumption for the cumulants of and is a restricted summability condition called -clustering property. One immediate application of the results is given by a stochastic process whose state is -clustering at any time t: then the above estimates can be applied with and and we obtain uniform in t estimates for the summability of time-correlations of the field. The above clustering assumption is obviously satisfied by any -clustering stationary state of the process, and our original motivation for the control of the summability of time-correlations comes from a quest for a rigorous control of the Green-Kubo correlation function in such a system. A key role in the proof is played by the properties of non-Gaussian Wick polynomials and their connection to cumulants.
Subject: 111 Mathematics
Rights:


Files in this item

Total number of downloads: Loading...

Files Size Format View
coupled_fields.pdf 429.2Kb PDF View/Open

This item appears in the following Collection(s)

Show full item record