Birthday Inequalities, Repulsion, and Hard Spheres

  title={Birthday Inequalities, Repulsion, and Hard Spheres},
  author={Will Perkins},
  journal={arXiv: Probability},
  • Will Perkins
  • Published 2015
  • Mathematics, Physics
  • arXiv: Probability
  • We study a birthday inequality in random geometric graphs: the probability of the empty graph is upper bounded by the product of the probabilities that each edge is absent. We show the birthday inequality holds at low densities, but does not hold in general. We give three different applications of the birthday inequality in statistical physics and combinatorics: we prove lower bounds on the free energy of the hard sphere model and upper bounds on the number of independent sets and matchings of… CONTINUE READING
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