Random walks on discrete cylinders and random interlacements
Random walks on discrete cylinders and random interlacements
复制标题
离散圆柱上的随机游走和随机交错
DOI：
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发表时间：
2008
期刊：
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通讯作者：
A. Sznitman
中科院分区：
文献类型：
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作者：
A. Sznitman
本文研究了柱面上简单随机游动迹线的局部图像与随机图的关系 2008年10月20日，在北京市人民政府办公厅（
http://www.math.ethz.ch/u/sznitman/preprints).特别是，我们表明，对于大N在附近的一个点的圆柱体的垂直分量的顺序Nd的补充访问的一组点的步行时间的顺序N2d是接近分布的法律的空的一组随机交错的水平，这是由一个独立的布朗当地时间。本文还导出了多点邻域内局部图像联合分布的极限性质。
AbstractWe explore some of the connections between the local picture left by the trace of simple random walk on a cylinder $${(mathbb {Z} / Nmathbb {Z})^d imes mathbb {Z}}$$ , d ≥ 2, running for times of order N2d and the model of random interlacements recently introduced in Sznitman (
http://www.math.ethz.ch/u/sznitman/preprints). In particular, we show that for large N in the neighborhood of a point of the cylinder with vertical component of order Nd the complement of the set of points visited by the walk up to times of order N2d is close in distribution to the law of the vacant set of random interlacements with a level which is determined by an independent Brownian local time. The limit behavior of the joint distribution of the local pictures in the neighborhood of finitely many points is also derived.