论文标题
吉布斯集合分区的限制形状
Limit shapes for Gibbs partitions of sets
论文作者
论文摘要
这项研究扩展了对整数分区的极限形状的先前研究，该图是基于对几何随机变量总和的分析。在这里，我们计算了集合分区的宏伟典型吉布斯集合的极限形状，这导致了泊松随机变量的总和。在轻度的单调性假设下，我们研究了各种能量的渐近行为引起的所有可能场景，还计算了极限形状是步骤函数的情况的局部极限形状曲线。
This study extends a prior investigation of limit shapes for partitions of integers, which was based on analysis of sums of geometric random variables. Here we compute limit shapes for grand canonical Gibbs ensembles of partitions of sets, which lead to the sums of Poisson random variables. Under mild monotonicity assumptions, we study all possible scenarios 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.
