论文标题
非电向布朗桥的边缘通用性
Edge Universality for Nonintersecting Brownian Bridges
论文作者
论文摘要
在本文中，我们研究了非质量的布朗桥的极端颗粒的波动，从$ a_1 \ leq a_2 \ leq a_2 \ leq \ cdots \ cdots \ leq a_n $ at time $ t = 0 $，结束至$ b_1 \ leq b_1 \ leq b_2 \ leq b_2 \ leq \ leq \ cdots \ cdots \ leq b_n $ at time $ t = 1 $ t = 1 $ t = 1 $ t = 1 $ t = 1 $ t = 1 $ t = 1 $ t = 1 $ t = 1 $， $μ_{a_n} =（1/n）\ sum_ {i}δ_{a_i}，μ_{b_n} =（1/n）\sum_iδ_{b_i} $是概率度量的离散化$μ_A，μ__b$。在$μ_a，μ_b$的规律性假设下，我们将粒子数量$ n $表示为无限，在任何时候$ 0 <t <1 $的极端颗粒的波动，在适当的重新恢复后，渐近地是通用的，融合到了空气点过程中。
In this paper we study fluctuations of extreme particles of nonintersecting Brownian bridges starting from $a_1\leq a_2\leq \cdots \leq a_n$ at time $t=0$ and ending at $b_1\leq b_2\leq \cdots\leq b_n$ at time $t=1$, where $μ_{A_n}=(1/n)\sum_{i}δ_{a_i}, μ_{B_n}=(1/n)\sum_i δ_{b_i}$ are discretization of probability measures $μ_A, μ_B$. Under regularity assumptions of $μ_A, μ_B$, we show as the number of particles $n$ goes to infinity, fluctuations of extreme particles at any time $0<t<1$, after proper rescaling, are asymptotically universal, converging to the Airy point process.
