Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiple equilibria of nonhomogeneous Markov chains and self-validating
  web rankings   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.

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The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg