@article{EJP1803,
author = {Graham Brightwell and Malwina Luczak},
title = {Vertices of high degree in the preferential attachment tree},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {17},
year = {2012},
keywords = {random graphs; web graphs; concentration of measure; martingales; preferential attachment},
abstract = {We study the basic preferential attachment process, which generates a sequence of random trees, each obtained from the previous one by introducing a new vertex and joining it to one existing vertex, chosen with probability proportional to its degree. We investigate the number $D_t(\ell)$ of vertices of each degree $\ell$ at each time $t$, focussing particularly on the case where $\ell$ is a growing function of $t$. We show that $D_t(\ell)$ is concentrated around its mean, which is approximately $4t/\ell^3$, for all $\ell \le (t/\log t)^{-1/3}$; this is best possible up to a logarithmic factor.},
pages = {no. 14, 1-43},
issn = {1083-6489},
doi = {10.1214/EJP.v17-1803},
url = {http://ejp.ejpecp.org/article/view/1803}}