书呆子狙击手问题

arXiv - MATH - Probability Pub Date : 2024-09-09 DOI:arxiv-2409.06068

Boris Alexeev, Dustin Mixon

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摘要

我们纠正了陶和吴在《恶性相邻问题》一文中出现的错误。我们试图解决以下问题。假设 N 个书呆子均匀地随机分布在一个正方形区域中。下午 3 点 14 分，每个书呆子都同时 "攻击 "了他们最近的邻居。在$N\to\infty$的极限中，毫发无损的书呆子的预期比例$P_N$是多少？

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The nerd snipers problem

We correct errors that appear throughout "The vicious neighbour problem" by Tao and Wu. We seek to solve the following problem. Suppose Nnerds are distributed uniformly at random in a square region. At 3:14pm, every nerd simultaneously snipes their nearest neighbor. What is the expected proportion $P_N$ of nerds who are left unscathed in the limit as $N\to\infty$?

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arXiv - MATH - Probability

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