Large deviations analysis for random combinatorial partitions with counter terms

Article Physics, Multidisciplinary

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

Stefan Adams et al.

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.

ANNALES HENRI POINCARE (2021)

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Article Physics, Mathematical

Limit Shapes for Gibbs Partitions of Sets

Ibrahim Fatkullin et al.

Summary: This study extends a prior investigation of limit shapes for grand canonical Gibbs ensembles of partitions of integers, which was based on analysis of sums of geometric random variables. It computes limit shapes for partitions of sets, which lead to the sums of Poisson random variables under mild monotonicity assumptions on the energy function. All possible limit shapes arising from different asymptotic behaviors of the energy are derived, and local limit shape profiles are computed for cases in which the limit shape is a step function.

JOURNAL OF STATISTICAL PHYSICS (2021)

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Article Statistics & Probability