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Weak Multiplex Percolation - Gareth J. Baxter, Rui A. da Costa, Sergey N. Dorogovtsev, José F. F. Mendes

Weak Multiplex Percolation

Buch | Softcover
75 Seiten
2022
Cambridge University Press (Verlag)
978-1-108-79107-6 (ISBN)
CHF 29,65 inkl. MwSt
In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However, percolation is not trivially generalised to multiple layers. This Element describes a generalisation of percolation to multilayer networks: weak multiplex percolation.
In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially generalised to multiple layers. This Element describes a generalisation of percolation to multilayer networks: weak multiplex percolation. A node belongs to a connected component if at least one of its neighbours in each layer is in this component. The authors fully describe the critical phenomena of this process. In two layers with finite second moments of the degree distributions the authors observe an unusual continuous transition with quadratic growth above the threshold. When the second moments diverge, the singularity is determined by the asymptotics of the degree distributions, creating a rich set of critical behaviours. In three or more layers the authors find a discontinuous hybrid transition which persists even in highly heterogeneous degree distributions, becoming continuous only when the powerlaw exponent reaches $1+1/(M-1)$ for $M$ layers.

1. Introduction; 2. Weak multiplex percolation; 3. Relation to other percolation models; 4. Critical phenomena with rapidly decaying degree distributions; 5. Critical phenomena with broad degree distributions; 6. Conclusions; References.

Erscheinungsdatum
Reihe/Serie Elements in the Structure and Dynamics of Complex Networks
Zusatzinfo Worked examples or Exercises
Verlagsort Cambridge
Sprache englisch
Maße 151 x 228 mm
Gewicht 93 g
Themenwelt Mathematik / Informatik Informatik Theorie / Studium
Mathematik / Informatik Mathematik Angewandte Mathematik
Naturwissenschaften Physik / Astronomie Thermodynamik
ISBN-10 1-108-79107-7 / 1108791077
ISBN-13 978-1-108-79107-6 / 9781108791076
Zustand Neuware
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