论文标题
KPZ型波动指数，用于平衡相互作用的扩散
KPZ-type fluctuation exponents for interacting diffusions in equilibrium
论文作者
论文摘要
我们考虑通过潜在的$ V $相互作用的$ n $扩散系统。我们研究了一个“高度函数”，对于特殊选择$ v（x）= \ e^{ - x} $，与固定的半分化聚合物的分区函数相吻合，也称为（固定的）O'Connell-yor聚合物。对于一般的平滑凸电势（概括了O'Connell-Yor情况），我们通过证明对$ n^{2/3} $方差的上限和下限匹配来获得高度函数波动的顺序，这是位于KPZ通用类中的模型的预期规模。我们研究的模型预计不会集成，我们的方法是分析性和非扰动性的，不使用显式公式或O'Connell-Yor聚合物的任何结果。
We consider systems of $N$ diffusions in equilibrium interacting through a potential $V$. We study a "height function" which for the special choice $V(x) = \e^{-x}$, coincides with the partition function of a stationary semidiscrete polymer, also known as the (stationary) O'Connell-Yor polymer. For a general class of smooth convex potentials (generalizing the O'Connell-Yor case), we obtain the order of fluctuations of the height function by proving matching upper and lower bounds for the variance of order $N^{2/3}$, the expected scaling for models lying in the KPZ universality class. The models we study are not expected to be integrable and our methods are analytic and non-perturbative, making no use of explicit formulas or any results for the O'Connell-Yor polymer.
