O 'Connell-Yor聚合物自由能的中心矩
Central moments of the free energy of the O'Connell-Yor polymer
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聚合物的自由能的方差增长由指数$2/3$控制，这是KPZ普适类模型的特征。我们开发精确的公式高斯积分的基础上的部分相关的累积量的自由能，$\log Z_{n,t}^θ$，期望的产品淬火累积量的时间的第一次从边界到系统，$s_0$。然后，我们使用这些公式来获得估计的$k$ -th中心矩的$\log Z_{n,t}^θ$以及$s_0$的$k$ -th退火时刻的$k> 2$，接近最佳的指数$(1/3)k+ε$和$(2/3)k+ε$，分别。
英文摘要：
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.
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