论文标题
确定过程和随机统治
Determinantal Processes and Stochastic Domination
论文作者
论文摘要
我们证明了与有限秩投影核相关的确定过程的随机支配。结果首先是由Lyons在离散环境中证明的。我们避免使用矩阵的机械，以获取在一般环境中起作用的证据。我们证明了两个决定性过程的随机支配，其中代表了不同度量的内核。将此结果与Lyons的定理结合在随机统治上，我们在$ \ Mathbb {Z}^2 $ at I.I.D上的最后一段段落中获得了最后一段时间的随机支配。几何重量。
We prove the stochastic domination for determinantal processes associated with finite rank projection kernels. The result was first proved by Lyons in discrete setting. We avoid the machinery of matroids in order to obtain a proof that works in a general setting. We prove another result on the stochastic domination of two determinantal processes where the kernels are represented with respect to different measures. Combining this result with Lyons' theorem on the Stochastic domination we obtain a result on the stochastic domination for the last passage time in a directed last passage percolation on $\mathbb{Z}^2$ with i.i.d. geometric weights.
