zbMATH — the first resource for mathematics

Orthogonal decompositions and functional limit theorems for random graph statistics. (English) Zbl 0810.05001
Mem. Am. Math. Soc. 534, 78 p. (1994).
In recent years Svante Janson, motivated by questions about distribution of subgraph counts in random graphs, developed a powerful technique of obtaining functional limit theorems for a broad class of random graph statistics. The underlying idea is to decompose a given function into a sum of orthogonal terms, for which a limit joint distribution can be established by means of a convergence theorem of Jean Jacod and Albert N. Shiryaev for continuous time martingales.
This deep monograph, 78 pages long, written with ease and perfection, describes the method in detail. Several illustrations and applications are provided.

05-02 Research exposition (monographs, survey articles) pertaining to combinatorics
05C80 Random graphs (graph-theoretic aspects)
60F05 Central limit and other weak theorems
PDF BibTeX Cite
Full Text: DOI