论文标题
O'Connell-Yor聚合物的自由能的中心时刻
Central moments of the free energy of the O'Connell-Yor polymer
论文作者
论文摘要
Seppäläinen和valkó在\ cite {sv}中表明，对于适当的参数选择，固定的O'Connell-Yor聚合物的自由能的差异增长受指数$ 2/3 $的约束，$ 2/3 $，KPZ通用类中模型的特征。 我们基于零件的高斯集成而开发精确的公式，以将自由能的累积物（$ \ log z_ {n，t}^θ$）与对第一个从边界跳入系统中的Quenched累积物的产物的期望，即$ s_0 $。然后，我们使用这些公式来获取$ k $ -th中央时刻$ \ log z_ {n，t}^θ$的估计，以及$ k $ -th的$ k $ s_0 $ for $ k> 2 $的$ s_0 $，分别具有几乎最佳的指数$（1/3）k+ε$和$（2/3）K+（2/3）K+ε$。
Seppäläinen and Valkó showed in \cite{SV} that for a suitable choice of parameters, the variance growth of the free energy of the stationary O'Connell-Yor polymer is governed by the exponent $2/3$, characteristic of models in the KPZ universality class. We develop exact formulas based on Gaussian integration by parts to relate the cumulants of the free energy, $\log Z_{n,t}^θ$, to expectations of products of quenched cumulants of the time of the first jump from the boundary into the system, $s_0$. We then use these formulas to obtain estimates for the $k$-th central moment of $\log Z_{n,t}^θ$ as well as the $k$-th annealed moment of $s_0$ for $k> 2$, with nearly optimal exponents $(1/3)k+ε$ and $(2/3)k+ε$, respectively.
