量子理想气体最大粒子能量的涨落与无规分配
Fluctuation of maximal particle energy of quantum ideal gas and random partitions
摘要：
研究了乘性统计量下大整数随机分拆中最大和项涨落的极限分布。我们表明，对于一个大家庭的吉布斯措施分区（所谓的广义玻色-爱因斯坦统计），这种分布是众所周知的Gumbel分布，通常出现在独立的随机变量的背景下。特别地，它意味着在$d$维量子理想气体的巨正则系综中单个粒子的（适当重新标度的）最大能量在极限中具有Gumbel分布。我们还应用我们的结果来寻找一个随机的三维杨氏图（平面划分）的高度的波动和调查下的广义玻色-爱因斯坦统计的随机分区的顺序统计。
英文摘要：
We investigate the limiting distribution of the fluctuations of the maximal summand in a random partition of a large integer with respect to a multiplicative statistics. We show that for a big family of Gibbs measures on partitions (so called generalized Bose--Einstein statistics) this distribution is the well-known Gumbel distribution which usually appears in the context of indepedent random variables. In particular, it means that the (properly rescaled) maximal energy of an individual particle in the grand canonical ensemble of the $d$-dimensional quantum ideal gas has the Gumbel distribution in the limit. We also apply our result to find the fluctuations of the height of a random 3D Young diagram (plane partition) and investigate the order statistics of random partitions under generalized Bose--Einstein statistics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
