The Min Mean-Weight Cycle in a Random Network

@article{Mathieu2013TheMM,
  title={The Min Mean-Weight Cycle in a Random Network},
  author={Claire Mathieu and David Bruce Wilson},
  journal={Combinatorics, Probability and Computing},
  year={2013},
  volume={22},
  pages={763 - 782}
}
  • C. Mathieu, D. Wilson
  • Published 19 January 2012
  • Mathematics
  • Combinatorics, Probability and Computing
The mean weight of a cycle in an edge-weighted graph is the sum of the cycle's edge weights divided by the cycle's length. We study the minimum mean-weight cycle on the complete graph on n vertices, with random i.i.d. edge weights drawn from an exponential distribution with mean 1. We show that the probability of the min mean weight being at most c/n tends to a limiting function of c which is analytic for c ≤ 1/e, discontinuous at c = 1/e, and equal to 1 for c > 1/e. We further show that if the… 
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