Work

Asymptotic normality of the k-core in random graphs

Year: 2008

Type: article

Abstract: We study the k-core of a random (multi)graph on n vertices with a given degree sequence. In our previous paper [Random Structures Algorithms 30 (2007) 50–62] we used properties of empirical distributions of independent random variables to give a simple proof of the fact that the size of the giant k-core obeys a law of large numbers as n→∞. Here we develop the method further and show that the fluctuations around the deterministic limit converge to a Gaussian law above and near the threshold, and to a non-normal law at the threshold. Further, we determine precisely the location of the phase transition window for the emergence of a giant k-core. Hence, we deduce corresponding results for the k-core in G(n, p) and G(n, m).

Source: The Annals of Applied Probability

DOI: 10.1214/07-aap478

Authors: Svante Janson, Malwina J. Luczak

Institutions: Uppsala University, London School of Economics and Political Science

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: Uppsala Universitet

OpenAlex ID: W2112406046