具有半平坦初值的随机增长的精确公式
Exact formulas for random growth with half-flat initial data
摘要：
从每个正偶格点被初始占据的特殊初始数据出发，得到了空间一点上非对称简单排它过程的高度函数的矩和母函数的精确公式.这些公式补充了E. Lee [J. Stat. 140（2010）635-647]，但是，与那些公式不同，我们的公式原则上适用于渐近性。我们还解释了我们的公式是如何相关的发散级数公式的半平坦KPZ的Le Doussal和Calabrese [J。Mech.2012（2012）P06001]，我们也使用本文的方法回收。这些生成函数是作为一个级数给出的，没有任何明显的弗雷德霍姆行列式或Pfronan结构.在长时间极限下，形式渐近性表明波动由Airy $_{2\to1}$边缘给出.
英文摘要：
We obtain exact formulas for moments and generating functions of the height function of the asymmetric simple exclusion process at one spatial point, starting from special initial data in which every positive even site is initially occupied. These complement earlier formulas of E. Lee [J. Stat. Phys. 140 (2010) 635-647] but, unlike those formulas, ours are suitable in principle for asymptotics. We also explain how our formulas are related to divergent series formulas for half-flat KPZ of Le Doussal and Calabrese [J. Stat. Mech. 2012 (2012) P06001], which we also recover using the methods of this paper. These generating functions are given as a series without any apparent Fredholm determinant or Pfaffian structure. In the long time limit, formal asymptotics show that the fluctuations are given by the Airy$_{2\to1}$ marginals.
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