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arXiv · 2303.11486

Non-rigidity Properties of the Coulomb Gas

Eric Thoma
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Abstract

We prove existence of infinite volume $d$-dimensional Coulomb gases which are not number rigid for $d \geq 3$. This makes the Coulomb gas the Gibbs point process with the longest range pairwise interaction (i.e.\ with the smallest $s$ in the interaction kernel $g(x) = |x|^{-s}$) for which number non-rigidity has been proved in $d \geq 3$. We rule out properties stronger than number rigidity for the two-dimensional Coulomb gas.

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Eric Thoma. 2023-03-20. Non-rigidity Properties of the Coulomb Gas. https://arxiv.org/abs/2303.11486

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