The nerd snipers problem

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 $N\to\infty$?