Formation of infinite loops for an interacting bosonic loop soup

作者：Dickson, Matthew^*; Vogel, Quirin

来源：ELECTRONIC JOURNAL OF PROBABILITY, 2024, 29: 24.

DOI：10.1214/24-EJP1085

• Bose-Einstein condensation
• random interlacements
• loop soups

We compute the limiting measure for the Feynman loop representation of the Bose gas for a non mean-field energy. As predicted in previous works, for high densities the limiting measure gives positive weight to random interlacements, indicating the quantum Bose-Einstein condensation. We prove that in many cases there is a shift in the critical density compared to the free/mean-field case, and that in these cases the density of the random interlacements has a jump-discontinuity at the critical point.

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