We introduce a family of ‘spatial’ random cycle Huang–Yang–Luttinger (HYL)-type models in which the counter-term only affects cycles longer than some cut-off that diverges in the thermodynamic limit. Here, spatial refers to the Poisson reference process of random cycle weights. We derive large deviation principles and explicit pressure expressions for these models, and use the zeroes of the rate functions to study Bose–Einstein condensation. The main focus is a large deviation analysis for the diverging counter term where we identify three different regimes depending on the scale of divergence with respect to the main large deviation scale. Our analysis derives explicit bounds in critical regimes using the Poisson nature of the random cycle distributions.

我们介绍了一系列“空间”随机循环的Huang-Yang-Luttinger（HYL）类型的模型，其中逆项对循环的影响时间长于某些在热力学极限范围内发生变化的截止时间。这里，空间是指随机循环权重的泊松参考过程。我们推导了这些模型的大偏差原理和显式压力表达式，并使用速率函数的零值来研究Bose-Einstein凝聚。主要关注点是针对发散反向项的大偏差分析，在该分析中，根据相对于主要大偏差尺度的发散规模，我们确定了三种不同的制度。我们的分析使用随机周期分布的泊松性质推导了临界状态下的显式边界。