The statistical mechanics of the interlacement point process

在这个项目中，我们将为无界甚至无限长度欧几里得空间中随机路径点过程的统计力学新理论奠定基础。主要的新颖之处将是对大盒子中经验平稳场的三级大偏差的适当处理，包括将速率函数描述为一种新的极限熵密度。这将使在热力学极限下对凝聚态中相互作用的玻色气体进行数学上合理的几何描述成为可能——这是我们的主要例子，也是本研究的驱动力。我们计划用相互作用的相互作用过程来严格地描述凝析液。我们期望获得的理解在寻找玻色-爱因斯坦凝聚存在的证明这一公开问题的背景下也可能有用。

In this project, we will lay the foundations for a new theory of statistical mechanics for point processes of random paths in Euclidean space of unbounded and even infinite lengths. The main novelty will be a proper treatment of the level-three large deviations for the empirical stationary field in large boxes, including a description of the rate function as a new kind of limiting entropy density. This will make possible a mathematically sound geometric description of the interacting Bose gas in the condensation regime in the thermodynamic limit -- this is our main example and the driving force of this research. We plan to describe the condensate rigorously in terms of an interacting interlacement process. The understanding we expect to obtain might also be useful in the context of the open problem of finding a proof for the occurrence of Bose--Einstein condensation.