DLR Equations for the Superstable Bose Gas at any Temperature and Activity

We construct a thermodynamic limit for the grand canonical Bose gas in dimension $d\geqslant1$ (in its Feynman-Kac representation) with superstable interaction at any inverse temperature $β>0$ and any chemical potential $μ\in\mathbb{R}$. Our infinite volume model is naturally a distribution over configurations of finite loops and possibly interlacements. We prove the limiting process to solve a new class of DLR equations involving random permutations and Brownian paths.

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