LCN2 Seminar: Breaking of ensemble equivalence in complex networks
- vrijdag 26 oktober 2018
- Gorlaeus Building
2333 CC Leiden
- Science club
September 2018 seminar
Title: Breaking of ensemble equivalence in complex networks
In this talk I will speak about the phenomenon of breaking of ensemble equivalence in complex networks. For many system in statistical physics the microcanonical and canonical ensemble are equivalent in the thermodynamic limit, but not for all. The goal is to classify for which classes of complex networks with topological constraints, breaking of ensemble equivalence occurs. We consider the simple case in which we fix the number of links and then we move to the configuration model (we fix the degree of each vertex). Then we study a more general setting with an arbitrary number of intra-connected and inter-connected layers, thus allowing modular graphs with a multi-partite, multiplex, time-varying, block-model or community structure. We give a full classication of ensemble equivalence in the sparse regime, proving that break-down occurs as soon as the number of constrained degrees is extensive in the number of nodes, irrespective of the layer structure. In addition, we derive an explicit formula for the specific relative entropy and provide an interpretation of this formula in terms of Poissonisation of the degrees.
About the LCN2 seminar
This talk is part of a series of seminars organized within an ongoing scientific initiative called "Leiden Complex Networks Network (LCN2), which aims at bringing together scientists with a common interest in both theoretical models and empirical analyses of complex networks and random graphs. The LCN2 community that is being established shares the approach of using networks for describing real-world complex systems and aims at developing related analytical and numerical methods, while also being open to other research approaches for studying complex systems. The talks are designed for a broad audience, allowing for constructive exchanges of ideas between scientists from different disciplines. During and after the talk, some drinks and simple snacks are provided.