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Dimensional Phase Transition in Random Walk Loop Soup

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SSDW03 - Geometry, occupation fields, and scaling limits

We consider a system of closed random walk trajectories interacting by mutual repulsion. This probabilistic model is interesting in itself, but is also motivated by its connections to certain models in statistical mechanics, such as the Bose gas, the double dimer model, or the spin O(N) model. We prove the occurrence of macroscopic loops in dimension d>2 (joint with A. Quitmann, 2022) and the absence of macroscopic loops in dimension d=2 (joint with W. Wu, 2024).

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