论文标题
PACMAN域中平面离散绿色功能的收敛速率
Rates of Convergence for the Planar Discrete Green's Function in Pacman Domains
论文作者
论文摘要
我们在域中的简单随机步行绿色功能的收敛速率获得上限$ ne^{i（π-α/2）} $。速率取决于楔形的角度，这是最尖锐的可用结果在极端情况下提出的结果$α= 0 $和$α=π$。我们的证明使用随机步行和布朗运动之间的KMT耦合。
We obtain upper bounds for the rates of convergence for the simple random walk Green's function in the domains $D_α= D_α(n)=\{re^{iθ}\in \mathbb{C}:0 <θ<2π-α, 0<r<2n\}-z_0,$ where $z_0\in\mathbb{Z}^2$ is a point closest to $ne^{i(π-α/2)}$. The rate depends on the angle of the wedge and is what was suggested by the sharpest available results in the extreme cases $α=0$ and $α=π$. Our proof uses the KMT coupling between random walk and Brownian motion.
