How can a clairvoyant particle escape the exclusion process?
How can a clairvoyant particle escape the exclusion process?
复制标题
透视粒子如何逃脱排除过程？
DOI：
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发表时间：
2016
影响因子：
1.5
通讯作者：
A. Teixeira
中科院分区：
文献类型：
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作者：
Rangel Baldasso;A. Teixeira
在一维整数格上，在时间为零时，节点以概率$独立地放置在每个站点上。
ho在[0，1）$中，并使它们演化为一个简单的对称排斥过程.在时间零点，在原点放置一个目标。目标仅以整数倍移动，并且可以移动到距离其当前位置$R$以内的任何站点。还假设目标可以预测所有节点的未来移动。我们证明，对于$R$足够大（取决于$的值），
ho$）目标有可能以正概率永远避免被检测到。这个结果的证明使用了两个独立的成分。首先，我们建立了一个重正化方案，可以用来证明渗流依赖定向模型在一定的解耦条件。这个结果是一般性的，不依赖于模型的特性。作为应用，我们证明了我们的主要定理不同的动力学，如独立的随机游动和独立的更新链。我们还证明了存在的定向渗流的随机交错和其空集的大尺寸。证明的第二步是排除过程的时空解耦。
We study a detection problem in the following setting: On the one-dimensional integer lattice, at time zero, place nodes on each site independently with probability $
ho in [0,1)$ and let them evolve as a simple symmetric exclusion process. At time zero, place a target at the origin. The target moves only at integer times, and can move to any site that is within distance $R$ from its current position. Assume also that the target can predict the future movement of all nodes. We prove that, for $R$ large enough (depending on the value of $
ho$) it is possible for the target to avoid detection forever with positive probability. The proof of this result uses two ingredients of independent interest. First we establish a renormalisation scheme that can be used to prove percolation for dependent oriented models under a certain decoupling condition. This result is general and does not rely on the specifities of the model. As an application, we prove our main theorem for different dynamics, such as independent random walks and independent renewal chains. We also proof existence of oriented percolation for random interlacements and for its vacant set for large dimensions . The second step of the proof is a space-time decoupling for the exclusion process.