DLR equations, number-rigidity and translation-invariance for infinite-volume limit points of the 2DOCP

Thomas Leblé

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arXiv · 2410.04958

DLR equations, number-rigidity and translation-invariance for infinite-volume limit points of the 2DOCP

Thomas Leblé

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Abstract

We prove that, at arbitrary positive temperature, every infinite-volume local limit point of the two-dimensional one-component plasma (2DOCP, also known as Coulomb or log-gas, or jellium) satisfies a system of Dobrushin-Lanford-Ruelle (DLR) equations - in particular, we explain how to rigorously make sense of those despite the long-range interaction. We also show number-rigidity and translation-invariance of the limiting processes. This extends results known for the infinite Ginibre ensemble. The proofs combine recent results on finite 2DOCP's and classical infinite-volume techniques.

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Thomas Leblé. 2024-10-07. DLR equations, number-rigidity and translation-invariance for infinite-volume limit points of the 2DOCP. https://arxiv.org/abs/2410.04958

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