Growing Cayley trees described by Fermi distribution

Abstract

We introduce a model for growing Cayley trees with thermal noise. The evolution of these hierarchical networks reduces to the Eden model and the Invasion Percolation model in the limit $T\to 0$, $T\to \infty$ respectively. We show that the distribution of the bond strengths (energies) is described by the Fermi statistics. We discuss the relation of the present results with the scale-free networks described by Bose statistics.

References in corpus (1)

• Statistical mechanics of complex networks

Cited by in corpus (14)

• Network geometry with flavor: from complexity to quantum geometry
• The Shannon and the Von Neumann entropy of random networks with heterogeneous expected degree
• Interdisciplinary and physics challenges of Network Theory
• Complex Quantum Network Geometries: Evolution and Phase Transitions
• A statistical mechanics approach for scale-free networks and finite-scale networks
• Complex Quantum Networks: a Topical Review
• Complex Quantum Network Manifolds in Dimension $d>2$ are Scale-Free
• Supersymmetric multiplex networks described by coupled Bose and Fermi statistics
• Quantum statistics in Network Geometry with Fractional Flavor
• A unified framework for quasi-species evolution and stochastic quantization
• Size of quantum networks
• Real-Space Visualization of Quantum Phase Transition by Network Topology
• Quantum statistics and networks by asymmetric preferential attachment of nodes -- between bosons and fermions
• Fermionic Networks: Modeling Adaptive Complex Networks with Fermionic Gases