# Improved mixing condition on the grid for counting and sampling independent sets

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Due to the fact that there is not a standard theory for non-equilibrium behavior, it is useful to gain insight on these systems studying some archetypical models, such as the non-equilibrium lattice gas knew as the KLS model (Katz, Lebowitz and Spohn; Phys. Rev. B 28, 1665 (1983)). The KLS model...

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Equations describing the temporal dynamics of the order parameter Îž(t) of a metal-semiconductor phase transition and the density n(t) of electron-hole pairs in a Peierls system in a light field are obtained on the basis of the Lagrange equation for the phonon mode and the Liouville equation...

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We consider level-set percolation for the Gaussian free field on $${\mathbb{Z}^{d}}$$, d â‰¥ 3, and prove that, as h varies, there is a non-trivial percolation phase transition of the excursion set above level h for all dimensions d â‰¥ 3. So far, it was known that the corresponding...