Emergence of interlacements from the finite volume Bose soup

TL;DR

This paper demonstrates that, under certain conditions, the finite volume Bose loop soup converges to a combination of the Bosonic loop soup and random interlacements, revealing the emergence of interlacements from the Bose soup.

Contribution

It establishes the convergence of the finite volume Bose loop soup to a superposition of Bosonic loop soup and random interlacements, highlighting the emergence of interlacements at high density.

Findings

Convergence of Bose loop soup to interlacements and Bosonic loop soup.

Intensity of interlacements equals excess density above critical.

Results hold for both free and mean field cases.

Abstract

We show that, conditioned on the (empirical) particle density exceeding the critical value, the finite volume Bose loop soup converges to the superposition of the Bosonic loop soup (on the whole space) and the Poisson point process of random interlacements. The intensity of the latter is given by the excess density above the critical point. We consider both the free case and the mean field case.