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Orthogonal Decompositions and Functional Limit Theorems for Random Graph Statistics
Svante Janson

Memoirs of the American Mathematical Society
1994; 78 pp; softcover
Volume: 111
ISBN-10: 0-8218-2595-X
ISBN-13: 978-0-8218-2595-2
List Price: US$39
Individual Members: US$23.40
Institutional Members: US$31.20
Order Code: MEMO/111/534
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This book develops a method to obtain limit theorems for various functionals of random graphs. The method is based on a certain orthogonal decomposition. Janson's results include limit theorems for the two standard random graph models, \(G_{n,p}\) and \(G_{n,m}\), as well as functional limit theorems for the evolution of a random graph and results on the maximum of a function during the evolution. Janson obtains both normal and nonnormal limits, and the method provides an explanation for the appearance of nonnormal limits. Applications to subgraph counts and to vertex degrees are presented as examples.


Researchers in random graph theory and related fields. Possibly including some theoretical computer scientists.

Table of Contents

  • Foundations
  • Limit theorems
  • Examples
  • References
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