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 organization: | Department of Mathematics and Statistics Mathematical physics |
Date: | 2018-04 |
Language: | eng |
Number of pages: | 18 |
Belongs to series: | Journal of Statistical Physics |
ISSN: | 0022-4715 |
DOI: | https://doi.org/10.1007/s10955-018-2000-6 |
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 |
Peer reviewed: | Yes |
Usage restriction: | openAccess |
Self-archived version: | acceptedVersion |
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