[Submitted on 9 May 2026 (v1), last revised 29 Jul 2026 (this version, v2)]

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Abstract:We study the critical free Bose gas from a probabilistic perspective with a focus on the three-dimensional case. We show that, unlike in the subcritical and supercritical regime, the critical asymptotics depend on the second heat-trace coefficient $a_1$ and hence on the geometry and boundary conditions. For $a_1<0$, long loops occur on the scale $L^2\log L$ and yield Poisson--Dirichlet statistics; for $a_1<0$, such loops are suppressed and the relevant fluctuations are produced by the short-loop bulk. We also derive asymptotics for the partition function, the one-particle reduced density matrix, and loop statistics. The fluctuation limits are governed either by a regularized Fredholm determinant of the Green operator or by Gaussian local central limit theorems, depending on the boundary regime.

Submission history

From: Quirin Vogel [view email]
[v1] Sat, 9 May 2026 21:43:52 UTC (3,353 KB)
[v2] Wed, 29 Jul 2026 09:26:15 UTC (3,358 KB)

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