相互作用玻色子环汤中无穷环的形成

有限体积玻色汤中交织结构的涌现

Emergence of interlacements from the finite volume Bose soup

本文证明当粒子密度超过临界值时，有限体积玻色环汤收敛为全空间玻色环汤与随机交织泊松点过程的叠加，强度由过剩密度决定，并涵盖自由与平均场两种情形。

Cluster explorations of the loop soup on a metric graph related to the Gaussian free field

We consider the loop soup at intensity ${1\over 2}$ conditioned on having local time $0$ on a set of vertices with positive occupation field in their vicinities. We give a relation between this loop soup and the usual loop soup conditioned on its local times. We deduce a domain Markov property for the loop soup, in the vein of the discrete Markov property proved by Werner: when exploring a cluster, the bridges outside the cluster form a Poisson point process. We show how it is related to the property due to Le Jan that the local times of the loop soup are distributed as the squares of a Gaussi…

Inverting the coupling of the signed Gausssian free field with a loop soup

Lupu introduced a coupling between a random walk loop-soup and a Gaussian free field, where the sign of the field is constant on each cluster of loops. This coupling is a signed version of isomorphism theorems relating the square of the GFF to the occupation field of Markovian trajectories. His construction starts with a loop-soup, and by adding additional randomness samples a GFF out of it. In this article we provide the inverse construction: starting from a signed free field and using a self-interacting random walk related to this field, we construct a random walk loop-soup. Our construction…

临界平面布朗运动环汤中的奇偶性问题（或“自由平面玻色子去了哪里？”）

Parity questions in critical planar Brownian loop-soups (or "where did the free planar bosons go?")

该研究探讨临界二维布朗运动环汤的占据时间场与高斯自由场平方的关联，证明场无法确定环的访问点集，且稠密特殊点属环汤的条件概率为1/2，环分解也分两类各占1/2概率。

Large deviation analysis for classes of interacting Bosonic cycle counts

This paper studies probabilistic mean-field models for interacting bosons at a positive temperature in the thermodynamic limit with random particle density. In particular, we prove large deviation principles for empirical cycle counts in all our models, and as such generalise recent work in \cite{ACK} where upper and lower large deviation bounds do not match. Namely, on the one hand we generalise to the so-called grand canonical ensemble, and on the other hand, we consider classes of interaction potentials depending on the cycle counts which are not restricted to be positive. Our large deviati…

相互作用玻色气体的自由能：带有环和交织的变分描述

The free energy of the interacting Bose gas: a variational description with loops and interlacements

本文通过变分方法研究相互作用玻色气体的自由能，利用环和交织过程描述长环和短环，引入新的相对熵密度并证明其存在性。