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Limit Shapes for Gibbs Partitions of Sets
Journal of Statistical Physics ( IF 1.6 ) Pub Date : 2021-04-28 , DOI: 10.1007/s10955-021-02756-8
Ibrahim Fatkullin , Jianfei Xue

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. Here we compute limit shapes for partitions of sets, which lead to the sums of Poisson random variables. Under mild monotonicity assumptions on the energy function, we derive all possible limit shapes arising from different asymptotic behaviors of the energy, and also compute local limit shape profiles for cases in which the limit shape is a step function.



中文翻译:

集的Gibbs分区的极限形状

这项研究扩展了对整数分区的大规范吉布斯合奏的极限形状的先前研究,该研究基于对几何随机变量之和的分析。在这里,我们为集合的分区计算极限形状,这导致了泊松随机变量的总和。在能量函数的温和单调性假设下,我们推导了由能量的不同渐近行为引起的所有可能的极限形状,并且还针对极限形状为阶跃函数的情况计算了局部极限形状轮廓。

更新日期:2021-04-29
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