Dimensional Phase Transition in Random Walk Loop Soup

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• Lorenzo Taggi (University of Rome La Sapienza)
• Wednesday 30 October 2024, 11:45-12:45
• Seminar Room 1, Newton Institute.

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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).

This talk is part of the Isaac Newton Institute Seminar Series series.

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