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

TL;DR

This paper develops a rigorous thermodynamic limit for the grand canonical Bose gas with superstable interactions across all temperatures and chemical potentials, using a novel distribution over loop configurations.

Contribution

It introduces a new class of DLR equations involving random permutations and Brownian paths to describe the Bose gas in the thermodynamic limit.

Findings

Constructed a thermodynamic limit for the Bose gas with superstable interactions.

Proved the limiting process solves a new class of DLR equations.

Model is a distribution over finite loops and interlacements.

Abstract

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 $\beta>0$ and any chemical potential $\mu\in\mathbb{R}$. 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.