论文标题
布朗之旅的亚室间隔的区域波动
Area fluctuations on a subinterval of Brownian excursion
论文作者
论文摘要
布朗游览的区域波动是通过通风的分布来描述的，该分布在物理，数学和计算机科学的不同领域中发现了应用。在这里，我们概括了此分布，以描述布朗游览的\ emph {subinterval}上的面积波动。在问题的第一个版本中（模型1）未施加其他条件。在第二版（模型2）中，我们研究了整个间隔的偏移区域，在次间隔上的区域波动的分布。这两个版本都承认方便的路径融合配方。在模型1中，我们获得了子间隔区域分布的拉普拉斯变换的显式表达式。在这两种模型中，我们通过评估该区域分布的尾部来关注该区域的大偏差，有时考虑到指数前因素。当在模型2中的大面积上进行调节时，我们发现了次室区域分数的速率函数的两个奇异点。它们可以解释为第二和三阶的动态相变。
Area fluctuations of a Brownian excursion are described by the Airy distribution, which found applications in different areas of physics, mathematics and computer science. Here we generalize this distribution to describe the area fluctuations on a \emph{subinterval} of a Brownian excursion. In the first version of the problem (Model 1) no additional conditions are imposed. In the second version (Model 2) we study the distribution of the area fluctuations on a subinterval given the excursion area on the whole interval. Both versions admit convenient path-integral formulations. In Model 1 we obtain an explicit expression for the Laplace transform of the area distribution on the subinterval. In both models we focus on large deviations of the area by evaluating the tails of the area distributions, sometimes with account of pre-exponential factors. When conditioning on very large areas in Model 2, we uncover two singularities in the rate function of the subinterval area fraction. They can be interpreted as dynamical phase transitions of second and third order.
