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Cover: 9781108791076 | Weak Multiplex Percolation | Gareth J. Baxter (u. a.) | Taschenbuch
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Weak Multiplex Percolation
Taschenbuch von Gareth J. Baxter (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2022
Genre: Physik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
ISBN-13: 9781108791076
ISBN-10: 1108791077
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Baxter, Gareth J.
Da Costa, Rui A.
Dorogovtsev, Sergey N.
Hersteller: Cambridge University Press
Maße: 229 x 152 x 4 mm
Von/Mit: Gareth J. Baxter (u. a.)
Erscheinungsdatum: 12.01.2022
Gewicht: 0,089 kg
Artikel-ID: 120755993
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2022
Genre: Physik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
ISBN-13: 9781108791076
ISBN-10: 1108791077
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Baxter, Gareth J.
Da Costa, Rui A.
Dorogovtsev, Sergey N.
Hersteller: Cambridge University Press
Maße: 229 x 152 x 4 mm
Von/Mit: Gareth J. Baxter (u. a.)
Erscheinungsdatum: 12.01.2022
Gewicht: 0,089 kg
Artikel-ID: 120755993
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