Varadhan's decomposition of shift-invariant closed uniform forms for large scale interacting systems on general crystal lattices

2022/08/31 by Bannai, Kenichi, Sasada, Makiko
#55N91 #60J60 #70G40 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary: 82C22 #Probability (math.PR) #Secondary: 05C63

paper · doi:10.48550/arxiv.2208.14917

Abstract

We prove a uniform version of Varadhan decomposition for shift-invariant closed uniform forms associated to large scale interacting systems on general crystal lattices. In particular, this result includes the case of translation invariant processes on Euclidean lattices Z^d with finite range. Our result generalizes the result of arXiv:2009.04699 which was valid for systems on transferable graphs. In subsequent research, we will use the result of this article to prove Varadhan's decomposition of closed L²-forms for large scale interacting systems on general crystal lattices.

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