Publications - Published papers
Please find below publications of our group. Currently, we list 565 papers. Some of the publications are in collaboration with the group of Sonja Prohaska and are also listed in the publication list for her individual group. Access to published papers (
) is restricted to our local network and chosen collaborators.
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) is restricted to our local network and chosen collaborators.
If you have problems accessing electronic information, please let us know:©NOTICE: All papers are copyrighted by the authors; If you would like to use all or a portion of any paper, please contact the author.
Conservation laws for voter-like models on random directed networks
M. Angeles Serrano, Konstantin Klemm, Federico Vazquez, Victor M. Eguiluz, Maxi San Miguel
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Status: Published
J. Stat. Mech. (2009) P10024
Abstract
We study the voter model, under node and link update, and the
related invasion process on a single strongly connected component of a directed network. We
implement an analytical treatment in the thermodynamic limit using the
heterogeneous mean field assumption. From the dynamical rules at
the microscopic level, we find the equations for the
evolution of the relative densities of nodes in a given state on
heterogeneous networks with arbitrary degree distribution and
degree-degree correlations. We prove that conserved quantities as
weighted linear superpositions of spin states exist for all
three processes and, for uncorrelated directed
networks, we derive their specific expressions. We also discuss the
time evolution of the relative densities that decay exponentially
to a homogeneous stationary value given by the conserved quantity.
The conservation laws obtained in the thermodynamic limit for a system
that does not order in that limit determine the probabilities of reaching
the absorbing state for a finite system. The
contribution of each degree class to the conserved quantity is
determined by a local property. Depending on the dynamics, the
highest contribution is associated to influential nodes reaching a
large number of outgoing neighbors, not too influenceable ones
with a low number of incoming connections, or both at the same
time.
Note
arXiv:0902.1769 [cond-mat.dis-nn]