We study the susceptibility, i.e., the mean size of the component containing a random vertex, in a general model of inhomogeneous random graphs. This is one of the fundamental quantities associated to (percolation) phase transitions; in practice one of its main uses is that it often gives a way of determining the critical point by solving certain linear equations. Here we relate the susceptibility of suitable random graphs to a quantity associated to the corresponding branching process, and study both quantities in various natural examples.
@article{10_37236_2035,
author = {Svante Janson and Oliver Riordan},
title = {Susceptibility in inhomogeneous random graphs},
journal = {The electronic journal of combinatorics},
year = {2012},
volume = {19},
number = {1},
doi = {10.37236/2035},
zbl = {1243.05219},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2035/}
}
TY - JOUR
AU - Svante Janson
AU - Oliver Riordan
TI - Susceptibility in inhomogeneous random graphs
JO - The electronic journal of combinatorics
PY - 2012
VL - 19
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/2035/
DO - 10.37236/2035
ID - 10_37236_2035
ER -
%0 Journal Article
%A Svante Janson
%A Oliver Riordan
%T Susceptibility in inhomogeneous random graphs
%J The electronic journal of combinatorics
%D 2012
%V 19
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/2035/
%R 10.37236/2035
%F 10_37236_2035
Svante Janson; Oliver Riordan. Susceptibility in inhomogeneous random graphs. The electronic journal of combinatorics, Tome 19 (2012) no. 1. doi: 10.37236/2035
