 
Summary: Asymptotic Analysis for Personalized Web Search
Yana Volkovich and Nelly Litvak
Department of Applied Mathematics, University of Twente
PO Box 217, 7500 AE Enschede, The Netherlands
email:{y.volkovich, n.litvak}@ewi.utwente.nl
Abstract
Personalized PageRank is used in Web search as an importance mea
sure for Web documents. The goal of this paper is to characterize the
tail behavior of the PageRank distribution in the Web and other complex
networks characterized by power laws. To this end, we model the Page
Rank as a solution of a stochastic equation R
d
= N
i=1 AiRi + B, where
Ri's are distributed as R. This equation is inspired by the original defi
nition of the PageRank. In particular, N models the number of incoming
links of a page, and B stays for the user preference. Assuming that N
or B are heavytailed, we employ the theory of regular variation to ob
tain the asymptotic behavior of R under quite general assumptions on
the involved random variables. Our theoretical predictions show a good
