Finding blocks and other patterns in a random coloring of Z
Finding blocks and other patterns in a random coloring of Z
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在 Z 的随机着色中查找块和其他图案
DOI：
10.1002/rsa.v28:1
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发表时间：
2006
影响因子：
1
通讯作者：
S. Rolles
中科院分区：
文献类型：
--
作者：
Heinrich Matzinger;S. Rolles
设k =（k）k∈Z是独立同分布的。其中P（Sk = 0）= P（Sk = 1）= 1/2，设S：=（Sk）k∈ N 0是Z上保持的对称随机游动，且与λ无关.我们考虑沿随机行走路径S沿着观察到的景物，即过程（χk：= χ Sk）k∈ N 0。我们以很高的概率重建了块n的颜色和长度，块n是距离原点最近的长度≥ n的块，仅给定观测值（χk）k∈[0，2·33 n]。我们发现停止时间，停止随机步行者与高概率在特定的地方的风景，即在blockn和区间[-3n，3n]。此外，我们以很高的概率重建块n周围的3 n 0.2阶的长度的一个块，给定从块n的边界开始的随机步行者仅收集3个n 0.3个观测值。© 2005威利期刊有限公司随机结构算法，2006
Let ξ = (ξk)k∈Z be i.i.d. with P(ξk = 0) = P(ξk = 1) = 1/2, and let S: = (Sk)k∈N0 be a symmetric random walk with holding on Z, independent of ξ. We consider the scenery ξ observed along the random walk path S, namely, the process (χk := ξSk)k∈N0. With high probability, we reconstruct the color and the length of blockn, a block in ξ of length ≥ n close to the origin, given only the observations (χk)k∈[0,2·33n]. We find stopping times that stop the random walker with high probability at particular places of the scenery, namely on blockn and in the interval [-3n,3n]. Moreover, we reconstruct with high probability a piece of ξ of length of the order 3n0.2 around blockn, given only 3⌊n0.3⌋ observations collected by the random walker starting on the boundary of blockn. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006