Abstract
Scale-free networks are characterized by strong fluctuations
of node connectivities that profoundly affect dynamical processes
occurring on them. Usual simple mean-field treatments are not
sufficient to deal with these fluctuations and need to be
modified to explictly take into account the dependence on the degree,
leading to nontrivial heterogeneous mean-field theories.
We discuss the application and the limits of validity of heterogeneous
mean-field theory for absorbing phase-transitions, as the contact
process, and for ordering phenomena as the voter model and Glauber dynamics
at zero temperature.
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