{"title":"The nerd snipers problem","authors":"Boris Alexeev, Dustin Mixon","doi":"arxiv-2409.06068","DOIUrl":null,"url":null,"abstract":"We correct errors that appear throughout \"The vicious neighbour problem\" by\nTao and Wu. We seek to solve the following problem. Suppose Nnerds are distributed\nuniformly at random in a square region. At 3:14pm, every nerd simultaneously\nsnipes their nearest neighbor. What is the expected proportion $P_N$ of nerds\nwho are left unscathed in the limit as $N\\to\\infty$?","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"264 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.06068","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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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