Multiple equilibria of nonhomogeneous Markov chains and self-validating web rankings
| dc.creator | Akian, Marianne | |
| dc.creator | Gaubert, Stephane | |
| dc.creator | Ninove, Laure | |
| dc.date | 2007-12-04 | |
| dc.date.accessioned | 2026-07-07T08:47:11Z | |
| dc.date.available | 2026-07-07T08:47:11Z | |
| dc.description | PageRank is a ranking of the web pages that measures how often a given web page is visited by a random surfer on the web graph, for a simple model of web surfing. It seems realistic that PageRank may also have an influence on the behavior of web surfers. We propose here a simple model taking into account the mutual influence between web ranking and web surfing. Our ranking, the T-PageRank, is a nonlinear generalization of the PageRank. It is defined as the limit, if it exists, of some nonlinear iterates. A positive parameter T, the temperature, measures the confidence of the web surfer in the web ranking. We prove that, when the temperature is large enough, the T-PageRank is unique and the iterates converge globally on the domain. But when the temperature is small, there may be several T-PageRanks, that may strongly depend on the initial ranking. Our analysis uses results of nonlinear Perron-Frobenius theory, Hilbert projective metric and Birkhoff's coefficient of ergodicity. | |
| dc.description | 22 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/0712.0469 | |
| dc.identifier | http://arxiv.org/abs/0712.0469 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143509 | |
| dc.subject | Probability | |
| dc.subject | Dynamical Systems | |
| dc.subject | 15A51, 47H07, 15A48, 15A18, 47H12, 60J10, 68P20 | |
| dc.title | Multiple equilibria of nonhomogeneous Markov chains and self-validating web rankings | |
| dc.type | text |