Gaps in Discrete Random Samples

@inproceedings{Grbel2009GapsID,
  title={Gaps in Discrete Random Samples},
  author={Rudolf Gr{\"u}bel},
  year={2009}
}
Let (Xi)i∈N be a sequence of independent and identically distributed random variables with values in the set N0 of non-negative integers. Motivated by applications in enumerative combinatorics and analysis of algorithms we investigate the number of gaps and the length of the longest gap in the set {X1, . . . , Xn} of the first n values. We obtain necessary and sufficient conditions in terms of the tail sequence (qk)k∈N0 , qk = P (X1 ≥ k), for the gaps to vanish asymptotically as n→∞: these are… CONTINUE READING