An Explicit Large Deviation Analysis of the Spatial Cycle Huang-Yang-Luttinger Model

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.

Automated summary

This study introduces a family of 'spatial' random cycle Huang-Yang-Luttinger (HYL)-type models, focusing on deriving large deviation principles, explicit pressure expressions, and studying Bose-Einstein condensation using the zeroes of rate functions. The main emphasis is on a large deviation analysis for the diverging counter term, identifying three different regimes based on the scale of divergence with respect to the main large deviation scale. The analysis provides explicit bounds in critical regimes by leveraging the Poisson nature of the random cycle distributions.