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When are small subgraphs of a random graph normally distributed?
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  • Published: March 1988

When are small subgraphs of a random graph normally distributed?

  • Andrzej Ruciński1 

Probability Theory and Related Fields volume 78, pages 1–10 (1988)Cite this article

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Summary

LetG be a graph and letX n count copies ofG in a random graphK(n,p). The random variable\(\left( {X_n - E\left( {X_n } \right)} \right)/\sqrt {Var\left( {X_n } \right)} \) is asymptotically normally distributed if and only ifnp m→∞ andn 2 (1-p)→∞, wherem=max {e(H)/|H|:H∪G}. In addition to, and in connection with this main result we investigate the formula for Var (X n ) and the Poisson convergence ofX n .

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Adam Mickiewicz University, Poznań, Poland

    Andrzej Ruciński

Authors
  1. Andrzej Ruciński
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Additional information

Part of the research was done during the author's stay in Division of Mathematics and Science, St. John's University, Staten Island, New York

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Ruciński, A. When are small subgraphs of a random graph normally distributed?. Probab. Th. Rel. Fields 78, 1–10 (1988). https://doi.org/10.1007/BF00718031

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  • Issue Date: March 1988

  • DOI: https://doi.org/10.1007/BF00718031

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Random Graph
  • Count Copy
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