Orthogonal decompositions and functional limit theorems for random graph statistics / Svante Janson.

Format:

Book

Author/Creator:

Janson, Svante, author.

Series:

Memoirs of the American Mathematical Society ; Number 534.

Memoirs of the American Mathematical Society, 0065-9266 ; Number 534

Language:

English

Subjects (All):

Random graphs.

Central limit theorem.

Orthogonal decompositions.

Physical Description:

1 online resource (90 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 1994.

Language Note:

English

Summary:

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.

Contents:

""Contents""; ""Chapter I. Foundations""; ""1. Introduction""; ""2. Preliminaries""; ""Graphs""; ""The Skorokhod topology""; ""Subsequences""; ""Continuous time martingales""; ""Semimartingales""; ""Wick products""; ""3. The basic limit theorem""; ""4. The orthogonal decomposition""; ""Chapter II. Limit theorems""; ""5. Limits for G[sub(n,p)]""; ""6. Limits for G[sub(n,m)]""; ""7. Moment convergence""; ""8. Functional convergence""; ""9. The maximum""; ""Chapter III. Examples""; ""10. Subgraph counts""; ""11. Vertex degrees""; ""12. Further examples""; ""References""

Notes:

"September 1994, volume 111, number 534 (third of 5 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0113-4