用简单随机过程的局部观测确定映射的亏格
Determining the Genus of a Map by Local Observation of a Simple Random Process
摘要：
给定一个嵌入在可定向曲面上的图，构造并分析了一个由随机激励、随机节点和面平衡组成的过程。它示出，给定先验界g'的属和n'的节点数，可以确定属的表面从局部观察的过程中限制到任何连接的子图，不能从其余的图中分离少于16 g '节点。观测时间和计算时间是以n'^g '为单位的多项式。该过程在曲面上构造了轻微扰动的随机“离散解析函数"，分析中的关键事实是这样的函数不能在曲面的一大块上消失。
英文摘要：
Given a graph embedded in an orientable surface, a process consisting of random excitations and random node and face balancing is constructed and analyzed. It is shown that given a priori bounds g' on the genus and n' on the number of nodes, one can determine the genus of the surface from local observations of the process restricted to any connected subgraph which cannot be separated from the rest of the graph by fewer than 16g' nodes. The observation time and the computation time are polynomial in n'^g'. The process constructs slightly perturbed random ``discrete analytic functions'' on the surface, and the key fact in the analysis is that such a function cannot vanish on a large piece of the surface.
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